Sum of 20 terms of the series 1+2+3+4+5+8+7+16+9+....... is

$(a)\;98+2^9\qquad(b)\;98+2^{10}\qquad(c)\;98+2^{11}\qquad(d)\;None\;of\;these$

Answer : (c) $\;98+2^{11}$
Explanation : every odd term is an AP of odd noumber and every even number is a GP of power of 2.
10 terms are AP of odd number and 10 terms are GP of common difference 2.
$sum=\frac{10(1+19)}{2}+\frac{2(2^{10}-1)}{2-1}$
$=100+2^{11}-2$
$=98+2^{11}.$