Find the sums given below:
$-5 + (-8) + (-11) + ….. + (-230)$

Given:

Given sequence is $(-5) + (-8) + (-11) + ……. + (-230)$.

To do:

We have to find the sum of $(-5) + (-8) + (-11) + ……. + (-230)$.

Solution:

Here,

\( (-5)+(-8)+(-11)+\ldots+(-230) \) is in A.P.

\( a=-5, d=-8-(-5)=-8+5=-3 \) and \( l=-230 \)

We know that,

\( a_{n}=a+(n-1) d \) \( \Rightarrow-230=-5+(n-1)(-3) \) \( \Rightarrow-230=-5-3 n+3 \) \( 3 n=-5+3+230=228 \) \( n=\frac{228}{3}=76 \) \( \mathrm{S}_{n}=\frac{n}{2}[a+l] \) \( =\frac{76}{2}[-5+(-230)] \) \( =38(-5-230) \)

\( =38 \times(-235)=-8930 \)

Therefore, the sum of the given sequence is $-8930$.