# geo sequence

• July 25th 2012, 11:04 AM
dannyc
geo sequence
1, 2, 4, 8, 16

In the above sequence, the first term is 1 and each term after the first is twice the preceding term. What is the sum of the 16th, 17th, and 18th terms?

I know 2^15 + 2^16 + 2^17 is the sum but how can I express it as 7(2^15)?
• July 25th 2012, 11:32 AM
earboth
Re: geo sequence
Quote:

Originally Posted by dannyc
1, 2, 4, 8, 16

In the above sequence, the first term is 1 and each term after the first is twice the preceding term. What is the sum of the 16th, 17th, and 18th terms?

I know 2^15 + 2^16 + 2^17 is the sum but how can I express it as 7(2^15)?

$2^{15} + 2^{16} + 2^{17} = 2^{15}+2^1 \cdot 2^{15} + 2^2 \cdot 2^{15}$

Factor out $2^{15}$.