# Solutions

Get detailed explanations to advanced GMAT questions.

### Question

A certain computer program generates a sequence of numbers a1, a2, … , an such that a1 = a2 = 1 and ak = ak-1 + 2ak-2 for all integers k such that 3 ≤ k ≤ n. If n > 6, then a7 = ?

Option A:

32

Option B:

43

Option C:

64

Option D:

100

Option E:

128

### Difficulty Level

Medium### Solution

Option B is the correct answer.

### Option Analysis

Ak= A(k-1) + 2* A(k-2)

A1= 1 and A2= 1

A(3)= A(3-1) + A(3-2)

=> = A(2) + 2(A1)

=> = 1 + 2*1 A(3)= 3

And with similar pattern,

A(4)= 3 + 2*1 = 5

A(5)= 5 + 2*3 = 11

A(6)= 11 + 2*5 = 21

A(7)= 21 + 2*11 = 43

### Related Questions

- If (2^x) (2^y) = 8 and (9^x)(3^y) = 81, then (x,y) equals:

- If T is a list of consecutive integers in increasing order, what is the sum of integers in T?

- A certain machine produces 1,000 units of product P per hour. Working continuously at this constant rate…

- A farmer who grows strawberries defines a “workday yield” as the number of litres of strawberries that…

- Each signal that a certain ship can make is comprised of 3 different flags hanging vertically in a…