Question

The sum of terms of the AP 34 + 32 + 30 + .... + 10 is .

• A. 290
• B. 286
• C. 280
• D. 284

Answer 1

The correct option is B 286

The formula to find the $n^{th}$ term of an arithmetic progression is $t_n=a+(n-1)d$
Where,
'$a_1$' is the first term,
'd' is the common difference,
'n' is the no. of terms,
'$t_n$' is the $n^{th}$ term.

Here,
$a_1$ = 34
$a_2$ = 32
d = $a_2$ - $a_1$ = 32 - 34 = -2
$t_n$ = 10

Substituting the given values in the equation to find the $n^{th}$ term, we get

$10=34+(n-1)(-2)$
$(n-1)(-2)=-24$
$n-1=\frac{24}{2}=12$
$\Rightarrow$ $n=13$

Sum of n terms of an AP is given by,
$S_n=\frac{n}{2}$ (first term + last term)
$S_{13}=\frac{13}{2}(34+10)$
$\Rightarrow$ $S_{13}=286$