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  • Tell me? The sum of all two digit positive numbers which when divided by 7 yeild 2 or5 as remainder is :

The sum of all two digit positive numbers which when divided by 7 yeild 2 or5 as remainder is  :

  • Option 1)

    1256

  • Option 2)

    1465

  • Option 3)

    1365

  • Option 4)

    1356

Answers (1)

best_answer

 

Summation of series of natural numbers -

\sum_{k=1}^{n}K= \frac{1}{2}n\left ( n+1 \right )
 

- wherein

Sum of first n natural numbers

1+2+3+4+------+n= \frac{n(n+1)}{2}

From the concept ,

General term will be 

T_{1}=7r+2

\sum_{r=2}^{13}(7r+2)=7\cdot \frac{2+13}{2}\times 6+2\times 12=654

T_{2}=7r+5

\sum_{r=2}^{13}(7r+5)=7\cdot \frac{1+13}{2}\times 13+5\times 13=702

total = 1356


Option 1)

1256

Option 2)

1465

Option 3)

1365

Option 4)

1356
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