A sequence of numbers satisfies the equation $A_n=2\cdot A_{n-1}+1.$ If $A_4=10,$ what is the value of $A_1?$

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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 » Thu Jul 30, 2020 8:37 am

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A sequence of numbers satisfies the equation $A_n=2\cdot A_{n-1}+1.$ If $A_4=10,$ what is the value of $A_1?$

A. 0.375
B. 1.375
C. 1.75
D. 4.5
E. 9

[spoiler]OA=A[/spoiler]

Source: Princeton Review

Source: Beat The GMAT — Problem Solving | Thu Jul 30, 2020 8:37 am

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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: A sequence of numbers satisfies the equation $A_n=2\cdot A_{n-1}+1.$ If $A_4=10,$ what is the value of $A_1?$

by Scott@TargetTestPrep » Wed Aug 05, 2020 10:15 am

Vincen wrote: ↑
Thu Jul 30, 2020 8:37 am
A sequence of numbers satisfies the equation $A_n=2\cdot A_{n-1}+1.$ If $A_4=10,$ what is the value of $A_1?$

A. 0.375
B. 1.375
C. 1.75
D. 4.5
E. 9

[spoiler]OA=A[/spoiler]

Solution:

Since A(4) = 2 * A(3) + 1, we have:

10 = 2 * A(3) + 1

9/2 = A(3)

4.5 = A(3)

Since A(3) = 2 * A(2) + 1, we have:

4.5 = 2 * A(2) + 1

3.5/2 = A(2)

1.75 = A(2)

Since A(2) = 2 * A(1) + 1, we have:

1.75 = 2 * A(1) + 1

0.75/2 = A(1)

0.375 = A(1)

Answer: A

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