Q : 7     Find the sum of first \small 22 terms of an AP in which \small d=7 and \small 22nd term is \small 149.

Answers (1)

It is given that
\small a_{22}=149,d=7,n = 22
Now, we know that
a_{22} = a+21d
149 = a+21\times 7
a = 149 - 147 = 2
Now, we know that 
S_n = \frac{n}{2}\left \{ 2a+(n-1)d \right \}
\Rightarrow S_{22}= \frac{22}{2}\left \{ 2\times(2) +(22-1)7\right \}
\Rightarrow S_{22}= 11\left \{ 4 +147\right \}
\Rightarrow S_{22}= 11\left \{ 151\right \}
\Rightarrow S_{22}= 1661
Therefore, there are 22 terms  and their sum is 1661

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