Question

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

Answer 1

Answer:

24th term

Step-by-step 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:

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

So:

$600 = \frac{n}{2}[2*2 + (n - 1)*2]$

$600 = \frac{n}{2}[4 + 2n - 2]$

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

$n = 24$