Question

The third term of an A.P. is $7$ and its $7$th term is $2$ more than thrice of its $3$rd term. Find the first term, common difference and the sum of its first $20$ terms.

Answer 1

$S_{3^{rd}}=7$

$S_7=2+3\times 7$

$S_7=2+21$

$S_{7^{th}}=23$

$a+2d=7$

$a+6d=23$

___________

$---$

$-4d=-16$

$d=4$ common diff.

$a+8=7$

$a=-1$ first term

$S_{20}=\frac{n}{2}[2a+(n-1\left)d\right]$

$=\frac{20}{2}[2x-1+(20-1\left)4\right]$

$=10[-2+76]$

$=10\times 74=740$