Question

Find the number of terms of the A.P $-12,-9,-6,.....,21$. If $1$ is added to each term of this A.P., then find the sum of all terms of the A.P thus obtained.

• A. $10,66$
• B. $12,66$
• C. $14,66$
• D. None of these

Answer 1

The correct option is B $12,66$

From given series, we have,

$a_n=a+(n-1)d$

$21=-12+(n-1)3$

$n=\frac{21+12}{3}+1$

$\therefore n=12$

upon adding $1$ to the series, we get,

$-11,-8,-5,.............,22$

$S_n=\frac{n}{2}(a+l)$

$S_n=\frac{12}{2}(-11+22)$

$\therefore S_n=66$