The sum of the first 20 terms common between | vedclass

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(B) The first series is $3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, \dots$ with common difference $d_1 = 4$.The second series is $1, 6, 11, 16,

Vedclass · Accepted Answer

$4020$

Vedclass · Answer

(B) The first series is $3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, \dots$ with common difference $d_1 = 4$.The second series is $1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, \dots$ with common difference $d_2 = 5$.The first common term is $11$.The common difference of the new series formed by common terms is $LCM(d_1, d_2) = LCM(4, 5) = 20$.Thus,the common terms form an Arithmetic Progression with first term $a = 11$ and common difference $d = 20$.The sum of the first $n$ terms is given by $S_n = \frac{n}{2}[2a + (n - 1)d]$.For $n = 20$,$S_{20} = \frac{20}{2}[2(11) + (20 - 1)20]$.$S_{20} = 10[22 + 19 	imes 20] = 10[22 + 380] = 10[402] = 4020$.

The sum of the first $20$ terms common between the series $3 + 7 + 11 + 15 + \dots$ and $1 + 6 + 11 + 16 + \dots$ is

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