The sequence $a_1, a_2, a_3, a_4, a_5$ is such that $a_n=a_{n-1}+5$ for $2 \le n \le 5.$ If $a_5=31,$ what is

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Fri Jul 10, 2020 3:19 am

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The sequence $a_1, a_2, a_3, a_4, a_5$ is such that $a_n=a_{n-1}+5$ for $2 \le n \le 5.$ If $a_5=31,$ what is the value of $a_1?$

(A) 1
(B) 6
(C) 11
(D) 16
(E) 21

[spoiler]OA=C[/spoiler]

Source: Official Guide

Source: Beat The GMAT — Problem Solving | Fri Jul 10, 2020 3:19 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: The sequence $a_1, a_2, a_3, a_4, a_5$ is such that $a_n=a_{n-1}+5$ for $2 \le n \le 5.$ If $a_5=31,$ what i

by deloitte247 » Sun Jul 12, 2020 6:24 am

$$Given\ that:\ a_n=a_{n-1}+5\ when\ 2\le n\le5$$
$$if\ n=2$$
$$a_2=a_{2-1}+5$$
$$a_2=a_1+5$$
$$and\ a_1=a_2-5$$
$$so\ the\ formula\ for\ this\ sequence\ can\ be\ rephrased\ as\ a_n=a_{n+1}-5$$
$$a_5=31$$
$$a_4=a_5-5=31-5=26$$
$$a_3=a_4-5=26-5=21$$
$$a_2=a_3-5=21-5=16$$
$$a_1=a_2-5=16-5=11$$
$$Answer\ =\ C$$

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: The sequence $a_1, a_2, a_3, a_4, a_5$ is such that $a_n=a_{n-1}+5$ for $2 \le n \le 5.$ If $a_5=31,$ what i

by Scott@TargetTestPrep » Sun Jul 19, 2020 10:39 am

Vincen wrote: ↑
Fri Jul 10, 2020 3:19 am
The sequence $a_1, a_2, a_3, a_4, a_5$ is such that $a_n=a_{n-1}+5$ for $2 \le n \le 5.$ If $a_5=31,$ what is the value of $a_1?$

(A) 1
(B) 6
(C) 11
(D) 16
(E) 21

[spoiler]OA=C[/spoiler]

Source: Official Guide

Solution:

Manipulating the equation, we have a(n - 1) = a(n) - 5 for 2 ≤ n ≤ 5. Now, let’s work backward:

Since a(5) = 31, then a(4) = a(5) - 5 = 31 - 5 = 26.

Since a(4) = 26, then a(3) = a(4) - 5 = 26 - 5 = 21.

Since a(3) = 21, then a(2) = a(3) - 5 = 21 - 5 = 16.

Since a(2) = 16, then a(1) = a(2) - 5 = 16 - 5 = 11.

Answer: C

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