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Sum of N Terms of an AP

Find the sum ...

Question

Find the sum of first $22$ terms of an AP in which $d = 7$ and $22 n d$ term is $149$ .

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Solution

$a_{22} = 149 = a + 7 \times 21$
$\Rightarrow 149 - 147 = 2 = a$
Now, $S_{22} = \frac{22}{2} (2 + 149) = 11 \times 151 = 1661$

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