Question

Find the sum of first $22$ terms of an A.P. where $d=7$ and the ${22}^{nd}$ term is $149$.

Answer 1

Here the values for $d=7$ and $t_{22}=149$. Mathematically, this can be written as $t_n=a+(n-1)d$

i.e. $149=a+21\times 7$

Or $a=149-147=2$

Thus, using now the formula for the sum of $n$ terms of the arithmetic progression, we have $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$.

Or, substituting the values we have $S_{22}=\frac{22}{2}[2\times 2+21\times 7]=11[4+147]$

Thus, $S_{22}=1661$.