Consider the sequence b_1, b_2, b_3, ...., b_… | GMAT Sprint

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PS · Problem Solving

sub-505

Sequences

Consider the sequence $b_1$ , $b_2$ , $b_3$ , ...., $b_n$ defined by $b_n = 7 + b_{n – 1}$ for every integer n ≥ 2. Given that $b_1 = 15$ , what is the value of $b_{40}$ ?

Answer Choices

Correct answer marked below

287

288

Correct

289

290

291

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Explanation

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Official Explanation

Official

We start with

b_1 = 15

and the common difference

d = 7

. The formula for the nth term is [m]b_n =…

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Comments

PeeyushDec 29, 2024

Great

IoleOct 1, 2024

thankss

DanielJul 10

This one is basically plug and chug, just find the pattern and you're good.

SaloniJul 14

yeah it's just arithmetic, nothing crazy here

AhmedJul 26

thanks, helpful. the answer choices being packed so close together is the real trap lol

NurmuhammadJun 22

super easy, common difference is just 7 so linear growth. done in 30 seconds

What this question tests

What it tests

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

Common trap

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

Consider the sequence b1b_1b1​, b2b_2b2​, b3b_3b3​, ...., bnb_nbn​ defined by bn=7+bn–1b_n = 7 + b_{n – 1}bn​=7+bn–1​ for every integer n ≥ 2. Given that b1=15b_1 = 15b1​=15, what is the value of b40b_{40}b40​?