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Find the sum of first $22$ terms of an AP in which $d=7$ and the $22$nd term is $149$.
A1540
B1617
C1694
D1711
Answer & Solution
Correct answer: B. 1617
First find the first term from $a_{22}=a+21d$:
$$149=a+21\cdot 7=a+147,$$
so $a=2$. Then
$$S_{22}=\frac{22}{2}[2a+(22-1)d]=11[4+147]=11\cdot 151=1661.$$
But check carefully: using $S=\frac{n}{2}(a+l)$ is simpler:
$$S_{22}=\frac{22}{2}(2+149)=11\cdot 151=1661.$$
Therefore the correct sum is $1661$.
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