set 26 q 8

[radhika1306]

In the sequence 1, 2, 4, 8, 16, 32, … , each term after the first is twice the previous term. What is
the sum of the 16th, 17th, and 18th terms in the sequence?
A. 2^18
B. 3 (2^17)
C. 7 (2^16)
D. 3 (2^16)
E. 7 (2^15)

[wizardofwashington]

In the sequence 1, 2, 4, 8, 16, 32, … , each term after the first is twice the previous term. What is
the sum of the 16th, 17th, and 18th terms in the sequence?
A. 2^18
B. 3 (2^17)
C. 7 (2^16)
D. 3 (2^16)
E. 7 (2^15)

IMO, the answer is E.
The sequence can be rewritten as 1, 2^1, 2^2, 2^3......2^15, 2^16,2^17 (the last three listed here are the 16th, 17th and 18th terms, which are of our interest).

The sum of the 16,17 & 18th terms = 2^15+2^16+2^17
= 2^15 (1+2+2^2)
= 2^15 (7)
Hence our answer should be E.

[kajcha]

Agree E

[radhika1306]

correct thanks

[camitava]

This is a GP (Geometric progression) and in GP to find out the nth number, the formula is -

Code: Select all

Tn = ar^(n - 1)

- where a = first term and r = common ratio.
So from this, you can get the 16, 17 and 18th number and sum them up and it will give the answer - E.