In the sequence S, each term after the first is twice the previous term. If the first term of sequence S is 3, what is the sum of the 14th, 15th, 16 and 17th terms in sequence S? Choose the correct option.
A) 3(2^16) B) 9(2^15) C) 21(2^14) D) 9(2^14) E) 45(2^13)
The terms in the sequence can be shown as   a(n) = 2^(n-1)* a   So, the sequence will look like: 3, 2*3, (2^2) *3,...   And the nth term will be given as 2^(n-1) *3   Therefore, a(14) = (2^13)*3, a(15) = (2^14) *3, a(16) = (2^15) *3 and a(17) = (2^16) *3   So, a(14) + a(15) + a(16)+a(17)= (2^13) *3 + (2^14) *3 + (2^15) *3+ (2^16) *3   = 3* (2^13) *(1+2+4+8) = 3* (2^13) *15   = 45 * (2^13)   Answer : 45(2^13)
<result>E</result>
In the sequence S, each term after the first is twice the previous term. If the first term of sequence S is 3, what is the sum of the 14th, 15th, 16 and 17th terms in sequence S?