Let $a_1, a_2, a_3, ..., a_n$ be a sequence of positive numbers where $a_1 = 1$ and for $n >= 1$ , $a_{n+1} = a_n + 4$ . Which of the following is the $n^{th}$ term in the sequence?

Correct answer marked below

4n - 3

Correct

4n - 1

4n

4n + 1

4n + 4

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Explanation

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Comments

Sarthak2d ago

Easy one, just plug in n=1. Only 4n-3 gives 1, so that's it.

Jongjust now

Yep, checking the first term is the fastest way to eliminate all the others.

Bhavya6h ago

Same. Took like 10 seconds.

VarshiniMay 27

Wait, is the formula for a_1 or a_0? I got confused because it says a_1=1 but the recurrence starts at n>=1.

GirirajMay 31

The n in the answer choices refers to the term number, so n=1 is the first term. Just test it.

RiyaAug 27

I set up a_2 = 1+4 = 5 and a_3 = 9, then tested each option. Only one matched for both.

HassanJun 19

Is this really 505-555? Seems more like a 400-level warmup.

AbidJul 2

Yeah, definitely on the easier side. Good confidence builder though.

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.

Let a1,a2,a3,...,ana_1, a_2, a_3, ..., a_na1​,a2​,a3​,...,an​ be a sequence of positive numbers where a1=1a_1 = 1a1​=1 and for n>=1n >= 1n>=1, an+1=an+4a_{n+1} = a_n + 4an+1​=an​+4. Which of the following is the nthn^{th}nth term in the sequence?