Q. 64.4( 26 Votes )

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

Answer :

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


13, 17, … 97


Since the common difference between the consecutive terms is constant. Thus, the above sequence is an A.P. with first term 13 and common difference 4.


Last Term of the A.P(l) = 97


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


It is known that the nth term of an A.P. is given by -


an = 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 -


Sn = (n/2)[a + l]


S22 = (22/2)[13 + 97]


= 11 × 110


= 1210


Thus, the required sum is 1210.


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