Question

The sum of 24 terms of the series $1,-3,4,-6,7,-9,10,...$ is

• A. 24
• B. -24
• C. 16
• D. -16

Answer 1

The correct option is B -24

The given series S can be divided into two sub-series $S_1$ and $S_2$
where $S_1=1,4,7,\mathrm{10..}$ and $S_2=-3,-6,-9,...$
24 terms of S would consist of first 12 terms of $S_1$ and first 12 terms of $S_2$
$\therefore$ Sum of $S$= Sum of $S_1$+ Sum of $S_2$

So using sum of A.P formula $S_n=\frac{n}{2}(2a+(n-1\left)d\right)$
$=\frac{12}{2}(2\times 1+11\times 3)+\frac{12}{2}(2\times -3+11\times -3)$
$=210-234=-24$