Sequence Question

[meg8887]

In the infinite sequence a1, a2, a3...an, each term after the first is equal to twice the previous term. If a5 - a2 = 12, what is the value of a1?

A) 4
B) 24/7
C) 2
D) 12/7
E) 6/7

Answer is E. How should I approach this problem?

[jigar24]

Let a1 be 'x'. Now, they have said the the common ratio between the terms is 2
Therefore,

If a1 = x, then,
a2 = 2x
a3 = 4x
a4 = 8x
a5 = 16x

They have given, a5 - a2 = 12
Therefore, 16x - 2x = 12
14x = 12
x = 6/7

Hope this helps.

Cheers!

[JonathanSchneider]

Perfect solution. In general, for sequence problems, draw out the slots that you need to fill: 1, 2, 3, 4, 5, etc., and label them below. Then list the value on top of each line. This helps to see the hidden connections.