The sum of the first 20 terms common between | vedclass

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Question

Given $n = 20;\,\,{S_{20}} = ?$

Series $\left( 1 ight) 	o 3,7,11,15,19,23,27,31,35,$

$39,43,47,$

$51,55,59...$

Series $\

Vedclass · Accepted Answer

$4020$

Vedclass · Answer

Given $n = 20;\,\,{S_{20}} = ?$

Series $\left( 1 ight) 	o 3,7,11,15,19,23,27,31,35,$

$39,43,47,$

$51,55,59...$

Series $\left( 2 ight) 	o 1,6,11,16,21,26,31,36,41,$

$46,51,56,$

$61,66,71.$

the common terms between both the series are

$11,13,51,71...$

Above series froms an Arithmetic progression $(A.P)$ 

Therefore, first term$(a)=11$ and

common difference $(d)=20$

Now, ${S_n} = \frac{n}{2}\left[ {2a + \left( {n - 1} ight)d} ight]$

${S_{20}} = \frac{{20}}{2}\left[ {2 	imes 11 + \left( {20 - 1} ight)20} ight]$

${S_{20}} = 10\left[ {22 + 19 	imes 20} ight]$

${S_{20}} = 10 	imes 402 = 4020$

$	herefore {S_{20}} = 4020$

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

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