2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = ?

2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = ?

A. 2^9
B. 2^10
C. 2^16
D. 2^35
E. 2^37

\(2+2=2*2=2^2\) (the sum of first and second terms);
\(2^2+2^2=2^3\) (the sum of previous 2 terms and the third term);
\(2^3+2^3=2^4\) (the sum of previous 3 terms and the fourth term);
...
The same will continue and finally we'll get \(2^8+2^8=2*2^8=2^9\), the sum of previous 8 terms and the 9th term.

Answer: A.

OR: we can identify that the terms after the first one represent geometric progression.

Sum of the terms of geometric progression is given by: \(Sum=\frac{a*(r^{n}-1)}{r-1}\), where \(a\) is the first term, \(n\) # of terms and \(r\) is a common ratio \(>1\).

In our original question we have 2 plus G.P. with 8 terms, so:

\(2+(2+2^2+2^3+2^4+2^5+2^6+2^7+2^8)=2+\frac{2*(2^{8}-1)}{2-1}=2^9\).

Answer: A.