Question

If the third term of an $A.P.$ is $7$ and its $7^{th}$ term is $2$ more than three times of its $3^{rd}$ term, then sum of its first $20$ terms is-

• A. $228$
• B. $74$
• C. $740$
• D. $1090$

Answer 1

The correct option is C $740$

We have,

$a_3=7$

$a+2d=7$ ---------(1)

$a_7=3a_3+2$

$a=?,d=?,S_{20}=?$

$a_7=3a_3+2$

$a+6d=3[a+2d]+2$

$a+6d=3a+6d+2$

$2a+2=0$

$a=-1$

put value $\left(a\right)$ in eqn $\left(1\right)$

$a+2d=7$

$-1+2d=7$

$2d=8$

$d=4$

$S_{20}=\frac{20}{2}[2a+19d]$

$S_{20}=10[-2+76]$

$S_{20}=740$

Hence this is the answer.