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

Plz answer

1 Answer

7 votes

Answer:

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

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