Find the sum of the first 35 terms of the following series, to the nearest integer.
3, 11, 19...

Answers

Answer 1
Answer:   4865

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

Explanation:

The sequence {3,11,19,...} is arithmetic since we are adding 8 to each term to get the next one

3+8 = 1111+8 = 19

etc. This means the common difference is d = 8.

The first term is a = 3

Let's use this formula

S = n*(2*a + d(n - 1) )/2

so we can find the sum of the first n terms. In this case, n = 35

So,

S = n*(2*a + d(n - 1) )/2

S = 35*(2*3 + 8(35 - 1) )/2

S = 35*(6 + 8(34))/2

S = 35*(6 + 272)/2

S = 35*(278)/2

S = 35*139

S = 4865

Answer 2

[tex]4865[/tex] is the  the sum of the first [tex]35[/tex] terms of the following series [tex]3, 11, 19...[/tex]

What is arithmetic sequence?

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2

The sequence  [tex]{3,11,19,...}[/tex]   is arithmetic since we are adding [tex]8[/tex] to each term to get the next one as shown below:

[tex]3+8 = 11\\11+8 = 19[/tex]

This means the common difference is [tex]d = 8.[/tex]

The first term is [tex]a = 3[/tex]

Number of terms [tex]=n=35[/tex]

Sum of the series

[tex]=\frac{n}{2} (2a+(n-1)d)[/tex]

[tex]=\frac{35}{2} (2[/tex]×[tex]3+34[/tex]×[tex]8)[/tex]

[tex]=35[/tex]×[tex]139[/tex]

[tex]=4865[/tex]

Hence, we can conclude that the sum of the first [tex]35[/tex] terms of the following series is [tex]4865[/tex]

Learn more about arithmetic sequence here:

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Answer:

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Answer:

Your answer is 2.5

Hope that this is helpful. Vote and like it

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Answer:

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Step-by-step explanation:

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Answer:

Your answer is 60

Hope that this is helpful. Tap the crown button, Like & Follow me

Answer: Hello! Your answer is.....

The area of the triangle is 60.

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The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing (in mm^3/s) when the diameter is 60 mm

Answers

Answer:

The volume is increasing at a rate of 1508 cubic millimeters per second when the diameter is 60 mm.

Step-by-step explanation:

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