Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

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#### Solution

The two-digit numbers, which when divided by 4, yield 1 as remainder, are

13, 17, … 97.

This series forms an A.P. with first term 13 and common difference 4.

Let *n* be the number of terms of the A.P.

It is known that the *n*^{th} term of an A.P. is given by, *a*_{n} = *a* + (*n* –1) *d*

∴97 = 13 + (*n* –1) (4)

⇒ 4 (*n* –1) = 84

⇒ *n* – 1 = 21

⇒ *n* = 22

Sum of *n* terms of an A.P. is given by,

Concept: Arithmetic Progression (A.P.)

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