Question

Question 21 (i)
Find the sum:
1 + (-2) + (-5) + (-8) + . . . + (-236)

Answer 1

Given,
a = 1, d = - 3 and l = -236
$a_n=a+(n-1)d\Rightarrow -236=1+(-3)\times (n-1)\Rightarrow 3\times (n-1)=237\Rightarrow n=1+\frac{237}{3}=1+79=80.$
$\therefore$ The number of terms in the AP is 80.
$\therefore$ Sum of n terms of an AP,
$S_n=\frac{n}{2}[a+l]\left[whereaisthefirsttermandlisthelastterm\right]$
$=\frac{80}{2}(1+(-236\left)\right)[\because n=80]$
$=40\times (-235)=-9400$