The two digit numbers which when divided by 4, yields 1 as remainder are 13, 17, 21, 25, ......, 97
This sequence forms an A.P. whose first term is 13 and difference is 4. Let 97 be the nth term of the A.P.
Then 97 = 13 + (n – 1) 4 ⇒ (n – 1) 4 = 97 – 13
⇒ (n – 1)4 = 84 ⇒ n – 1 = 21 ⇒ n = 22
Hence, the total number of terms are 22.
∴ Sum of 22 terms =

22

2

[(2 × 13) + (22 - 1)4]
i.e., S22 = 11 [26 + 84] = 1210