The sum of the first 20 terms common between the series 3+7+11+15+..... and 1+6+11+16+..... , is : Option 1) 4000 Option 2) 4020 Option 3) 4200 Option 4) 4220

N neha
S solutionqc

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Sum of n terms of an AP -

$S_{n}= \frac{n}{2}\left [ 2a +\left ( n-1 \right )d\right ]$

and

Sum of n terms of an AP

$S_{n}= \frac{n}{2}\left [ a+l\right ]$

- wherein

$a\rightarrow$ first term

$d\rightarrow$ common difference

$n\rightarrow$ number of terms

series are 3,7,11,15,19,23,27,31..............

and 1,6,11,16,21,26,31....................

So common terms are 11,31,............

$\therefore S_{20}= \frac{20}{2}\left [ 2\times 11+\left ( 20-1 \right )\times 20 \right ]$

$=10\left [ 22+380 \right ]$

$=10\left [402]$

$=4020$

Option 1)

4000

Option 2)

4020

Option 3)

4200

Option 4)

4220

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