Question

In an Ap if the sum of the first 10 terms is equal to the sum of first 20 terms, then the sum of first 30 terms is :

• A. 5
• B. 1
• C. 0
• D. 10

Answer 1

Answer:

C. 0

$S_{10}=S_{20}$

$\frac{n}{2}(2a+(n-1)d)$

$\frac{10}{2}(2a+(10-1)d$

$=\frac{20}{2}(2a+(20-1)d)$

$5(2a+9d)=10(2a+19d)$

$(2a+9d)=\frac{10}{5}(2a+19d)$

$(2a+9d)=2(2a+19d)$

$2a+9d=4a+38d$

$4a-2a+38d-9d=0$

$2a+29d=0$

$S_{30}=\frac{30}{2}(2a+(30-1)d)$

$15(2a+29d)=15(0)=0$