Question

Evaluate the given series $7+12+17+.....+102=$ .....

• A. $1020$
• B. $1090$
• C. $109$
• D. $2018$

Answer 1

The correct option is B $1090$

Series is $7+12+17+........+102$

which is in A.P. where,

First term $a=7$

and Common difference, $d=a_2-a_1=12-7=5$

and last term, $l=102$

Now, no. of terms, $n=?$

Let $102$ is $n$th term.

Now,

$a_n=a+(n-1)d=102$

$7+(n-1)5=102$

$5n+2=102$

$5n=100$

$n=20$

Sum of n terms,

$S_n=\frac{n}{2}(a+l)$

$S_n=\frac{20}{2}(7+102)$

$=1090$