Question 120

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

Solution

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The numbers will be of the form 7k+2, where k is a whole number.

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

So sum = 16+23+.... +93, which is 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 =  $$\frac{12}{2}\left(16+93\right)$$  = 654

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