Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder
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 is 4.
Let n be the number of terms of 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=n2[2a+(n−1)d]S22=222[2(13)+(22−1)(4)]=11[26+84]=1210
Thus the required sum is 1210.