The sequence A is defined by $A_n = A_{n-1} + 2$ for each integer $n ≥ 2$ , and $A_1 = 45$ . What is the sum of the first 100 terms in sequence A?

Correct answer marked below

243

14,400

Correct

14,500

24,300

24,545

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Comments

YuktaMay 25

Wait, this is just an arithmetic sequence right? Each term goes up by 2. So I can find the 100th term first and then use the average trick.

MelissaMay 31

Yep exactly, just use first + last over 2 times number of terms.

JasmineJun 8

For anyone confused: A1=45 and you add 2 each time. So A100 = 45 + 99*2. Then sum = 100*(45 + A100)/2.

TusharJun 20

Oh I almost used 100*2 instead of 99*2, thanks for pointing that out!

UtkarshJun 1

Got 14500 after working it out, took me a second to remember the formula but it's straightforward once you set it up.

AndreaJul 18

Is there a quick way to eliminate answer choices here? Like the sum has to be bigger than 100*45 since terms increase.

RafidJul 24

Yeah anything under 4500 is out immediately since each term is at least 45.

What this question tests

Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.

Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.

The sequence A is defined by An=An−1+2A_n = A_{n-1} + 2An​=An−1​+2 for each integer n≥2n ≥ 2n≥2, and A1=45A_1 = 45A1​=45. What is the sum of the first 100 terms in sequence A?