Find the sum of $20$ terms of an arithmetic progression (A.P) if its first term is $2$ and the seventh term is $20$.
First term of A.P $= a_1 = 2$ (Given)
Let the common difference of A.P $= d$
$n^{th}$ term of A.P $= a_n = a_1 + \left(n - 1\right) d$
$\therefore \;$ $7^{th}$ term of A.P $= a_7 = a_1 + 6d = 20$ (Given)
i.e. $\;$ $2 + 6d = 20$
i.e. $\;$ $6 d = 18$ $\implies$ $d = 3$
Sum of $n$ terms of A.P $= S_n = \dfrac{n \left[2a_1 + \left(n - 1\right) d\right]}{2}$
$\therefore \;$ Sum of $20$ terms of A.P $= S_{20} = \dfrac{20 \times \left[4 + \left(20 - 1\right) \times 3\right]}{2}$
i.e. $\;$ $S_{20} = 10 \times 61 = 610$