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