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  4. If the sum of the first 40 terms of the series, 3 + 4 + 8 + 9 + 1 3 + 14 + 18 + 19 + ... is (102)m, then m is equal to :

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Q. If the sum of the first 40 terms of the series, $3 + 4 + 8 + 9 + 1 3 + 14 + 18 + 19 + ...$ is $(102)m$, then m is equal to :

JEE MainJEE Main 2020Sequences and Series

Solution:

Sum of the 40 terms of
$3 + 4 + 8 + 9 + 13 + 14 + 18 + 19…$
$= (3 + 8 + 13 +…upto\, 20\, term)$
$+ [4 + 9 + 15 +… upto\, 20\, terms]$
$=10\left[\left\{6 + 19 × 5 + 8 + 19 × 5\right\}\right]$
$= 10 × 204 = 20 × 102$