Question

Two A.P's have the same common difference. If the first term of the two A.P's are $3$ and $8$ respectively, find the difference between their sum to first $30$ terms.

• A. $150$
• B. $100$
• C. $200$
• D. $50$

Answer 1

The correct option is A $150$

For first A.P
$S{1}_n=\left(\frac{n}{2}\right)(2n+(n-1\left)d\right)$
$S{1}_{30}=\left(\frac{30}{2}\right)(2\times 3+(30-1\left)d\right)$
$S{1}_{30}=15(6+29d)$
$S{1}_{30}=90+435d$
For second AP
$S{2}_n=\left(\frac{n}{2}\right)(2n+(n-1\left)d\right)$
$S{2}_{30}=\left(\frac{30}{2}\right)(2\times 8+(30-1\left)d\right)$
$S{2}_{30}=15(16+29d)$
$S{2}_{30}=240+435d$
Difference between $S{1}_{30}-S{2}_{30}=(90+435d)-(240+435d)=150$