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  • Find the sum of all the two digit numbers which leave the remainder 2 when divided by 5.  

Find the sum of all the two digit numbers which leave the remainder 2 when divided by 5.

 

Answers (1)

First two-digit number which gives remainder 2 after diving by 5=12

Last two-digit number which gives remainder 2 after dividing by 5=97

As we can see if we add 5 in 12 we will get 17 which will also give us remainder 2.

We could see the series will be 12,17,22,...........97

This is forming an AP with a=12

                                           d=5

                                           l=97

Now let's find the number of terms in this series

l=a+(n-1)d

\Rightarrow 97=12+(n-1)5

\Rightarrow (n-1)5=85

\Rightarrow (n-1)=17

\Rightarrow n=18

To find :

Sum of two-digit numbers which leave remainder 2 when divided by 5

Use sum formula of AP

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

\Rightarrow S_{n}=\frac{18}{2}[2\times 12+(18-1)5]

\Rightarrow S_{n}=9[24+85]=9\times 109

S_{n}=981

Sum of two-digit number which leaves remainder 2 when divided by 5 in 981

Posted by

Safeer PP

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