Question

8) How many terms of the arithmetic sequence (2, 4, 6, 8, ...} will give a sum of 600?

Plz answer

Answer 1

24th term

Explanation:

Given

`S_n = 600`

`Sequence:2,4,6,8..`

Required

Find n

First, calculate common difference d

`d = 4 -2 = 2`

Calculate n using:

`S_n = (n)/(2)[2a + (n - 1)d]`

So:

`600 = (n)/(2)[2*2 + (n - 1)*2]`

`600 = (n)/(2)[4 + 2n - 2]`

Multiply by 2

`120 = n[2 + 2n]`

`1200 = 2n^2 + 2n`

Rewrite as:

`2n^2 + 2n - 1200 = 0`

Divide by 2

`n^2 + n - 600 = 0`

Solve quadratic equation.

It gives:

`n = -25\ n = 24`

Since n can't be negative;

Then

`n = 24`