Question

The sum of first $9$ terms of an A.P is $351$ and the sum of its first $20$ terms is $1770$, Find the ${11}^{th}$ term.

• A. $90$
• B. $93$
• C. $96$
• D. $98$

Answer 1

Answer: (B)

$93$

Sum of $n$ terms of an AP $=\frac{n}{2}(2a+(n-1\left)d\right)$ where $a$ is the first term and $d$ is the common difference.

Sum of first $9$ terms $=\frac{9}{2}(2a+8d)=351$

$9(a+4d)=351⟹9a+36d=351$ --(1)

Sum of first $20$ terms $=\frac{20}{2}(2a+19d)=1770$

$2a+19d=177$---(2)

Solving (1) and (2), $a=3,d=9$

${11}^{th}$ term $=a+10d=3+90=93$