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If the sum of the first 40 terms of the series, $3 + 4 + 8 + 9 + 13 + 14 + 18 + 19...........$ is (102)m, then m is equal to:

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answer is A.

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Detailed Solution

$S = 3 + 4 + 8 + 9 + 13 + 14 + 18 + 19........40$ terms

$\Rightarrow S = 7 + 17 + 27 + 37 + 47 + .....20$ terms

$∴ S_{40} = \frac{20}{2} [2 \times 7 + (19) 10] = 10 [14 + 190] = 10 [2040] = (102) (20)$

$\Rightarrow m = 20$

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