An algebra problem by A Former Brilliant Member

Algebra Level 2

The sum of 100 consecutive odd integers is 20400. What is the sum of the lowest and highest numbers?


The answer is 408.

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A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Zee Ell
Jan 19, 2017

The sum of the first n terms of an arithmetic sequence:

S n = a 1 + a n 2 n S_n = \frac {a_1 + a_n}{2} n

In this case:

S n = 20400 and n = 100 S_n = 20400 \text { and } n = 100

20400 = a 1 + a n 2 × 100 20400 = \frac {a_1 + a_n}{2} ×100

a 1 + a n = 408 a_1 + a_n = \boxed {408}

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