Question 120

The sum of all two digit numbers that give a remainder 2 when they are divided by 7 is _______

Solution

$$\frac{12}{2}\left(16+93\right)$$The numbers will be of the form 7k+2 where k is an whole number.

The smallest two digit number is when k=2 which is 16 and the largest 2 digit number is 93 k= 13

So sum = 16+23+.... +93 which are in AP.

Sum to n terms of an AP= n/2(a+l), where n=number of terms , a=1st term ,l=last term

Here n=12 , a=16 , l=93

Hence sum = 654

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