Question

Find the sum of terms given below.

$34+32+30+.....+10$

Answer 1

We know,

$n^{th}$ term $a_n=a+(n-1)d$

$a=$ First term

$d=$ Common difference

$n=$ number of terms

$a_n=n^{th}$ term

Sum formula

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

Here $a=34,d=-2,a_n=10$

So, $10=34-2(n-1)$

$\Rightarrow 2(n-1)=24$

$\Rightarrow n-1=12$

$\Rightarrow n=13$

So, $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$S=\frac{13}{2}(68-24)=286$