Question

Find the sums given below:

$-5+(-8)+(-11)+......+(-230)$

• A. $-8930$
• B. $8769$
• C. $6778$
• D. $6667$

Answer 1

Answer: (A)

$-8930$

Given series can also be written as,

$-5-8-11-14-....-230$

It can be observed that difference between any two consecutive terms of the given series is constant and equal to $-3$.

Thus given series is an AP whose common difference and first term as $-5$ and $-3$ respectively.

As we know $n^{th}$ term is given as

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

& Sum of first $n$ terms, $S_n=\frac{n}{2}(a+l)$, where $a$ & $l$ are the first term & last term of an AP.

So, $a=-5,d=-3$

$\Rightarrow -230=-5-3(n-1)$
$\Rightarrow 3(n-1)=225$
$\Rightarrow n-1=75$
$\Rightarrow n=76$

Sum of first $n$ terms is given as,

$S_n=\frac{n}{2}(a+l)$, where $a$ & $l$ are the first term & last term of an AP.
Thus,

$S=\frac{76}{2}(-5+-230)=38\times (-235)=-8930$