Question

The sum of all two digit numbers which when divided by 4 yield unity as remainder is

Answer 1

Step-by-step explanation:

the number should be of the form 4k+1

Smallest 2 digit number that gives remainder 1 when divided by 4 ⇒ 13(when k=3) the first term of A.P

Largest 2 digit number that gives remainder 1 when divided by 4 ⇒ 97(when k=24) the last term of AP

Series: 13,17,21,....97

97=a+(n−1)d

97=13+(n−1)4

89=(n−1)4

(n−1)=21

n=22

Sum of series =

2

n

[first term + last term]

=

2

22

[13+97]

=11×(110)

=1210

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