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  • I need help with The sum of the first 20 terms common between the series 3+7+11+15+..... and 1+6+11+16+..... , is :

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

 

Answers (2)

best_answer

Use

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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solutionqc

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