Determine the number of terms n in each arithmetic series.
12) a1 = 13, d = 3, Sn = 1225

Answers

Answer 1

Answer:

The number of terms n in arithmetic series is n=25

Step-by-step explanation:

We are given:

a₁ = 13

d = 3

Sₙ = 1225

We need to find number of terms i.e n

The formula used will be: [tex]S_n=\frac{n}{2}(2a+(n-1)d)[/tex]

Putting values and finding n

[tex]S_n=\frac{n}{2}(2a+(n-1)d)\\1225=\frac{n}{2}(2(13)+(n-1)3)\\1225=\frac{n}{2}(26+3n-3)\\1225=\frac{n}{2}(23+3n)\\2(1225)=n(23+3n)\\2450=23n+3n^2\\3n^2+23n-2450=0[/tex]

Now, solving using quadratic formula to find value of n:

[tex]n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Putting values: a=3, b=23 and c=-2450

[tex]n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\n=\frac{-23\pm\sqrt{(23)^2-4(3)(-2450)}}{2(3)}\\n=\frac{-23\pm 173}{6}\\n=\frac{-23+ 173}{6}, n=\frac{-23- 173}{6}\\n=25, n=-\frac{98}{3}[/tex]

So, we get: [tex]n=25, n=-\frac{98}{3}[/tex]

Since number of terms can't be negative so, n= 25

So, the number of terms n in arithmetic series is n=25


Related Questions

Which of the following is NOT always true of a function and its inverse?

Answers

The statement that is not always true of inverse functions  is (d) f-1(x) is a function

What are inverse functions?

Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function

How to determine the statement that is not always true of inverse functions?

As mentioned above,

The inverse functions are the opposite of an original equation

This means that:

If a function is f(x), then the inverse if f-1(x)

However, all inverse equation are relations, but not all inverse equations are functions

This means that the statement that is not always true of inverse functions  is (d) f-1(x) is a function

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f(x) = x² + 3x
f(-4)=
evaluate the function

Answers

Answer:

4

Step-by-step explanation:

f(x) = x² + 3x

f(-4) = (-4)^2 + 3×(-4)

= 16 - 12

= 4

-2/3(3x - 4) +3x =5/6
What is X

X= -19/6
X= -11/6
X = 21/6
X=29/6

Answers

The value of x from the given linear function is -11/6

Linear equation

Linear equations are expression that has a leading degree of 1

Given the linear equation below

-2/3(3x - 4) +3x =5/6

Expand

-2/3(3x) - 2(-4) + 3x = 5/6

-2x + 8/3  + 3x = 5/6

Collect the like terms

x = 5/6 - 8/3

x = (5-16/6

x = -11/6

Hence the value of x from the given linear function is -11/6

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Maria drove 520 miles in 8 hours. How many miles per hour did she drive?

Answers

Answer:

65 mph

Step-by-step explanation:

520/8 is 65

this is an arithmetic progression. please help!

A graduate is required to pay his education loan of RM3960 in 24 monthly instalments, with the first instalment being RM 50. Subsequent instalments are increased by RM 10 each month. What is the amount of the last instalment?​

Answers

Answer:

The last installment is RM 280

=========================

Given

AP with:

The first term a = 50,Common difference d = 10,Number of terms n = 24.

Solution

Use the nth term equation of AP to find the last installment:

[tex]a_n=a_1+(n-1)d[/tex][tex]a_{24}=50+(24-1)(10) = 50+23*10=50+230=280[/tex]

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Answers

Answer:

2√23

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

Step 1: Define

We are given a right triangle. Therefore, we can use PT to solve for the missing length.

Step 2: Identify Variables

Leg a = √88

Leg b = 2

Hypotenuse c = x

Step 3: Solve for x

Substitute:                     (√88)² + 2² = x²Exponents:                    88 + 4 = x²Add:                               92 = x²Isolate x:                        √92 = xSimplify:                         2√23 = xRewrite:                         x = 2√23

Answer:

Mm did you do this already its been 4 days just want to make sureee

Step-by-step explanation:

I NEED HELP WITH BUMBER 3 PLEASE ASAP ILL LOVE U FOR EVER AND IF YOU CANT SEE THE WORDS VERY WELL THAN U CAN JUS ZOOM IN

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Step-by-step explanation:

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We know that f(x) is a positive, decreasing, and concave down function.

Therefore, the order, from least to greatest is:

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Answers

Answer:

-62

Step-by-step explanation:

One easy way to subtract two negative numbers like this (for me anyway) is to factor out the minus sign and add:

- (15 + 47)

- (62)

Remove the parentheses

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Which expression could be used to determine the product of -4 and 342
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x (
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Answers

Answer:

the second answer

Step-by-step explanation:

.........

Which value is closest to 0 on the number line?


A. 20

B. -21

C. |2|

D. |-3|

Answers

2

u r the very much welcome

Answer:

The answers C

Step-by-step explanation:

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Answers

Answer:

36

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Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Step-by-step explanation:

Step 1: Define

3pm

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Step 2: Evaluate

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Answer:

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Answers

Answer:

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Step-by-step explanation:

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Answers

by looking at the graph given we can see that:

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How to determine in which intervals the function increases, decreases or is constant?

Here our function is:

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Answers

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Suppose x = 9 is a solution to the equation f(x) = g(x). If a table of values for the equation y = f(x) contains an x-value of 9 and a corresponding y-value of 18, then which of these statements is correct about a table of values for the equation y = g(x)?


A
If it contains an x-value of 9, the corresponding y-value must be 9.

B
If it contains an x-value of 9, the corresponding y-value must be 18.

C
If it contains a y-value of 18, the corresponding x-value must be 9.

D
If it contains a y-value of 18, the corresponding x-value must be 18.

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Answer:

I think it may be A

Step-by-step explanation:

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Step-by-step explanation:

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And elephant's heart beats 28 times per minute. Complete
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840 beats in 30 minutes

Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

-1 and 1

Step-by-step explanation:

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I’m not sure but good luck with your test
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Max puts a stopper in the bathtub and turns on the faucet at t=0. After 5 minutes, there are 11 gallons of water in the tub and after 10 minutes, there are 22 gallons in the tub. Write an equation that relates the number of gallons, g, to the time, t. Does the relationship represent a linear function? Justify your response.

Answers

Answer:

y = 2.2x

Yes, it represents a linear function

Step-by-step explanation:

Given that :

Stopper applied at t = 0

At t = 5 minutes ; water in tub = 11 gallons

At t = 10 minutes ; water in tub = 22 gallons

General form of a linear function :

y = mx + c

Where c = intercept ; m = Slope ; y and x are dependent and independent variables respectively

The intercept = gallon of water at t = 0 ; this is not given and will be taken as 0

Slope = change in y / charge in x

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Slope = 11 / 5

Slope = 2.2

Hence ;

y = 2.2x + 0

y = 2.2x

Yes, it represents a linear function

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Answers

For 9:

1. Angle T and angle M are congruent because they are given

2. The line AH bisects angle THM because it is given

3. Angle 1 and angle 2 are congruent because of properties of angle bisection

4. The line AH is congruent to the line HA because of the reflexive property

5. Triangle TAH is congruent to triangle MHA because of AAS

6. The line TA is congruent to MA because of congruent triangles

For 10:

1. Angle H and angle J are congruent because it is given

2. G is the midpoint of FI because it is given

3. Angle 1 and angle 2 are congruent because they are vertical angles

4. Line HG is equal to line JG because of properties of midpoints

5. The triangles HIG and JFG are congruent because of AAS

6. The lines HI and JF are congruent because of congruent triangles

32. Which of the following best describes the relationship between AABC and ADEF? (1 point)
B
E
A
TH
D
F
O AACBAFED
O AABC ADEF
O AABC AEFD
O AABC ADFE

Answers

Answer:

2) tri ABC is congreunt to tri DEF

Step-by-step explanation:

you would have to make sure you name the traingles in a specific order so the congruent angles in both triangles are listed in the same order :))

The option that best describes the relationship between AABC and ADEF is AABC ~ ADEF, the correct option is B.

What are similar triangles?

All similar triangles are triangles that share these two features presented as follows;

1. Congruent angle measures.

2. Proportional side lengths.

We are given that;

AB is similar to DE: BC is similar to EF; AC is similar to DF; ZA is similar to ZD; ZB is similar to ZE; ZC is similar to ZF.

Now,

The relationship between two similar triangles is that their corresponding angles are equal and their corresponding sides are proportional1. This means that if AABC and ADEF are similar, then:

∠A = ∠D

∠B = ∠E

∠C = ∠F

AB/DE = BC/EF = AC/DF

To describe this relationship, we can use a notation that shows which angles and sides correspond to each other. For example, we can write:

AABC ~ ADEF

This means that triangle ABC is similar to triangle DEF and the order of the letters shows how they match up. The first letter of each triangle corresponds to the first angle, the second letter corresponds to the second angle, and so on.

Therefore, by similar triangle properties the answer will be AABC ~ ADEF.

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Answer:

-430

Step-by-step explanation:

Please help someone anyone please help

Answers

Answer:

if 135 calories represents 1/4 then a whole cup is 540 calories so two cups is 540 times 2 which is 1080

Step-by-step explanation:

Answer:

1080 calories

Step-by-step explanation:

135x8=1080

PLEASE HELP WILL MARK BRAINLIEST Question 8
Which pair of equations show below would have infinite solutions?
Answer
A Y = -2 + 8
y = 4x - 7
B y = x - 4
y = 3x - 2
C) x
x – 3y = -3
x – 3y = 6
D 3x +y = 3
6x + 2y = 6

Answers

Answer:

Step-by-step explanation:

a)y=-2x+8

y=4x-7

solution

b)y=x-4

y=3x-2

solution

c)x – 3y = -3

x – 3y = 6

no solution

d)3x +y = 3

6x + 2y = 6

infinite.

Answer: D

Step-by-step explanation:

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