Answer:
he arithmetic sequence ai is defined by the formula: a1= 2 ai= ai - 1 -3 find the sum of the first 335 terms in the sequence
Step-by-step explanation:
In an arithmetic sequence,
a_1=2a
1
=2
a_i=a_{i-1}-3a
i
=a
i−1
−3
To find:
The sum of the first 335 terms in the given sequence.
Solution:
The recursive formula of an arithmetic sequence is:
a_i=a_{i-1}+da
i
=a
i−1
+d ...(i)
Where, d is the common difference.
We have,
a_i=a_{i-1}-3a
i
=a
i−1
−3 ...(ii)
On comparing (i) and (ii), we get
d=-3d=−3
The sum of first i terms of an arithmetic sequence is:
S_i=\dfrac{i}{2}[2a+(i-1)d]S
i
=
2
i
[2a+(i−1)d]
Putting i=335,a=2,d=-3i=335,a=2,d=−3 , we get
S_{335}=\dfrac{335}{2}[2(2)+(335-1)(-3)]S
335
=
2
335
[2(2)+(335−1)(−3)]
S_{335}=\dfrac{335}{2}[4+(334)(-3)]S
335
=
2
335
[4+(334)(−3)]
S_{335}=\dfrac{335}{2}[4-1002]S
335
=
2
335
[4−1002]
S_{335}=\dfrac{335}{2}(-998)S
335
=
2
335
(−998)
On further simplification, we get
S_{335}=335\times (-499)S
335
=335×(−499)
S_{335}=-167165S
335
=−167165
Therefore, the sum of the first 335 terms in the given sequence is -167165.
write an equation of the line passing through point (3, -1) and perpendicular to y= -x+1
am I supposed to do the picture one or the you type
I need help on this problem
Answer:
x 1 / 2 / 3 / 4 / 5
y -3 / 3 / 11 / 21 / 33
you can figure this put by just putting the equation above in a calculator and replacing all the x's with numbers and press equal the answer is y
example
1^2 + 3(1) -7 = -3
x= 1
y=-3
and you can use those coordinates to graph them
(1,-3) (2,3) (3,11) (4,21) (5,33) and so on
IN NEED OF HELP LIKE ASAP!
Answer:
Below
Step-by-step explanation:
2^-3 / 2^2 is equal to 1 / 2^5
Write the expression in exponential form
2^-5 = 2^-5
Set the exponents as equal
-5 = -5
So this is true
Hope this helps! Best of luck <3
We know that corresponding angles of similar figures are congruent. Based on this example, are corresponding sides of similar figures always congruent?
Answer:
no
Step-by-step explanation:
similar figures means that the corresponding angles are congruent and the corresponding sides are similar. this means if ABCD and EFGH are similar, A=E*x, B=F*x, C=G*x, and D=H*x, so they aren't congruent
Anthony travels 48 miles by car in the same time it takes him to travel 12 miles on his
bike. His average rate of speed by car is 24 miles per hour faster than his average rate of speed by bike. What is the average rate of speed for both the car and the bike?
Answer:
Anthony's average speed by car is 32 miles per hour and his average speed by bike is 8 miles per hour.
Step-by-step explanation:
Let the average rate (in miles per hour) at which Anthony travels by car be c and by bike be b.
His average rate of speed by car is 24 miles per hour faster than his average rate of speed on bike. In other words:
[tex]c = b + 24[/tex]
Anthony travels 48 miles by car in the same amount of time it takes him to travel 12 miles by bike.
Recall that distance is given by the rate multiplied by the time t.
Hence, c multiplied by time t equals 48 miles:
[tex]\displaystyle ct = 48[/tex]
Likewise, b multiplied by the same time t equals 12 miles:
[tex]bt = 12[/tex]
Solve. We can multiply the second equation by four:
[tex]4bt = 48[/tex]
Substitute:
[tex]ct = 4bt[/tex]
Divide:
[tex]c = 4b[/tex]
Since c = b + 24:
[tex](b + 24) = 4b[/tex]
Solve for b. Subtract:
[tex]24 = 3b[/tex]
And divide:
[tex]b = 8\text{ miles per hour}[/tex]
Hence, Anthony bikes at an average rate of 8 miles per hour.
Since his average speed by car is 24 miles per hour faster, his average speed by car is 32 miles per hour.
In conclusion, Anthony's average speed by car is 32 miles per hour and his average speed by bike is 8 miles per hour.
Sofia is driving to Texas. She travels at 70 kilometers per hour for 2 hours, and 63 kilometers per hours for 5 hours. Over 7 hours time period what was sofia's average speed ?
Answer:
65 kph
Step-by-step explanation:
There were a total of 7 hours. So two hours were at 70 and the other 5 hours at 63: the equation would be: (70+70+63+63+63+63+63)/7=65
help please!!
angle 1 + angle 2 = ?
angle 7 + angle 8 = ?
angle 1 + angle 6 = ?
Answer:
angle 1 + angle 2 = ∠DEB
angle 7 + angle 8 = ∠NEG
angle 1 + angle 6 = ∠NEA
How would you find x?
Answer:
the value of x = 61
I hope it's helps you
6x+6=-5+3x+17
I need help
Answer:
Get all the terms with x on the left. Get all the terms without x on the right. Simplify by adding and subtracting the terms without x and adding and subtracting the terms with x. Finally divide to get the value of x.
Step-by-step explanation:
6x+6 =- 5+3x+17
6x+6 -6 =- 5+3x+17 -6
6x = 5+3x+11
6x = 3x + 16
6x - 3x = 3x + 16 -3x
3x = 16
3x / 3 = 16 / 3
x = 15/3 + 1/3
x = 5 1/3
x = 5.33333...
select all the ways that the sun supports life on earth
Answer:
all of the above
Step-by-step explanation:
Answer:
It gives heat and light on the earth.
plants makes food with the help of sunlight.
Animals take warmth by sunlight.etc.
The value of 45 is between what two numbers?
A.between 3 and 4
B.between 6 and 7
C.between 22 and 23
D.between 44 and 46
Answer:
D this will be your answer
d.between 44 and 46
for sure it is the correct answer
(4x-1)(x^2+3) step by step
Answer:
4x + x^2 + 3
Step-by-step explanation:
First you are gonna drop the parenthesis. Then you are gonna combine -1 and +3 which gives you +2.
PLEASE HELP ME FAST I WILL GIVE 30 POINTS AND BRAINLIEST AND HEART
Questions 10-12
f(x)= 3x-13
g(x)= 2x^2-4x-5
h(x)=4^x-7
10. Find (f - g) (x)
11. Find (f - h) (x)'
12. Find (f + g) (x)
(f–g)(x)= (3x-13) – (2x²–4x–5)= –2x²+7x-8
(f–h)(x)= (3x-13) – ( 4^x –7) = 3x – 4^x–6
(f+g)(x)= (3x-13) + (2x²–4x–5) = 2x²–x – 18
I hope I helped you^_^
Solve with steps:
2 cos(x) = square root 3 = 0 0
Convert the improper fraction to a mixed number. 32/3
Answer:
32/3 = 10 2/3
Step-by-step explanation:
8+ 2/3k-4/15k-1/4
Omg I can never figure this out need help
Answer:
2/5k + 31/4
Step-by-step explanation:
8+ 2/3k-4/15k-1/4
2/3k - 4/15k + 8 - 1/4
(5)(2/3k) - 4/15k + 8 - 1/4
10/15k - 4/15k + 31/4
6/15k + 31/4
2/5k + 31/4
Pls help I need it I’m really confused
The equations are alike because all of their variables are equivalent to 6. Another similarity is that they are all one-step equations, meaning they can be solved with just one operation.
[tex]4a=24\\a=6[/tex]
[tex]c-1.2=4.8\\c=6[/tex]
[tex].5b=3\\b=6[/tex]
[tex]d + 5.5=11.5\\d=6[/tex]
These equations are different because require different operations to find their variables. Their terms, excluding the variable, also have differnt values.
Have a nice day. Feel Free to ask Questions. Spread The Love.
what is 5tx+4t=???
????????????
Answer:
t(5x + 4)
Step-by-step explanation:
im not entirely sure if this is correct
Answer:
t×(5x+4)
Step-by-step explanation:
factor out t from the expression
[tex]\frac{\sqrt{a+b} }{\sqrt{a-b} } +\frac{\sqrt{a-b} }{\sqrt{a+b} }[/tex]
Answer:
[tex]\frac{(a+b)}{a^{2} -b^{2} }[/tex] + [tex]\frac{(a-b)}{a^{2} -b^{2} }[/tex] = [tex]\frac{2a}{a^{2} -b^{2} }[/tex]
Step-by-step explanation:
Step-by-step explanation:
[tex] \frac{ \sqrt{a + b} }{ \sqrt{a - b} } + \frac{ \sqrt{a - b} }{ \sqrt{a + b} } \\ squaring \: on \: both \: sides \\ \frac{a + b}{a - b} + \frac{a - b}{a + b} \\ \frac{(a + b) \times (a + b) + (a - b)(a - b)}{(a - b)(a + b)} \\ \frac{ {(a + b)}^{2} + {(a - b)}^{2} }{ {a}^{2} - {b}^{2} } \\ remaining \: in \: attachment[/tex]
[tex]thank \: you[/tex]
c. Mr. champing travels 20 km duo East and then 25 km due west. respect to find his position with respect to his starting point.
. Define opposite numbers.
Answer:
Opposite numbers are numbers that, when placed on a number line, are the exact same distance away from the 0, but on opposite sides, or in opposite directions. They look the same except for their signs.
this is based off what I know I hope it helps
please help
answer choices
A. (-5, 2)
B. (5, 2)
C. (2, -5)
D (-2, 5)
Answer:
The correct choice is option B. (5, 2)
Step-by-step explanation:
The rotation rule of 180° is = (x ,y) -> ( -x , -y) .
Coordinates of C before the rotation are ( -5 , -2) so according to the rule above they will now be = C'( 5 , 2 ) .
Therefore, the ordered pair for C' is (5, 2) after the 180 degrees rotation.
blue dot located on the number line?
Answer:
it's 4/5 cause no. of division is 5 and it's on 4 place therefore it's 4/5
Answer:
4/5 is the correct answer
find the possible formula for the nth term of sequence 7 11 15 9
Answer:
7, 11, 15, 19, 23, ... To get the terms in the original sequence, we need to add on 3 to each of the terms in the 4n sequence. Hence, the general formula for the nth term of the original sequence is 4n + 3.
hope this helped!!!
Factor out the greatest common factor. If the greatest common factor is 1, just retype the
polynomial.
9d^ 2 - 27d^ 5 + 45d^ 3
Answer:
Below.
Step-by-step explanation:
The GCF of 9 , 27 and 45 = 9.
GCF of the d terms is d^2.
So the GCF of the whole expression is 9d^2.
Factors are 9d^2( 1 - 3d^3 + 5d)
to complete a continuing pattern,identify pattern rule.true or false?
Answer:
true
Step-by-step explanation:
6+ 1 ( 7x17 )-7
im stuck
Answer:
118
Step-by-step explanation:
6+1(7×17)-7
=6+1(119)-7
=6+119-7
=125-7
=118
Please mark me brainliest.
Answer: 118
Step-by-step explanation:
Given expression
6 + 1 (7 × 17) - 7
Simplify values in the parentheses
=6 + 1 (119) - 7
Simplify by multiplication
=6 + 119 - 7
Simplify by addition/subtraction
=125 - 7
=[tex]\boxed{118}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
a shea cd player costs $80 last year and $112 this year. what was the percent of increase in its price
Answer:
40% increase
Step-by-step explanation:
c = final value - initial value
------------------------------------
initial value
112 - 80 = 32
32 / 80 = 0.4
0.4 = 40%
please help easy maths gradient thanks so much
Answer:
Y-2x=8
Y-x=8/2
Yx=4
Maths gradients
Answer:
b
Step-by-step explanation:
A club has 34 members，and 18 of them are new。If two new members quit the club，what percentage of the remaining people in the club are not new members？
Answer:
its still 34 bcs there were 18 new members and 2 left they were new not old so we didn't exactly touch the number 34 so yeah hope i'm correct
Step-by-step explanation: