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

Answer

N/a

Explanation

First number of two digit, leaves the remainder 1, when divided by 4 = 13
Similarly, last number of two digit, leaves the remainder 1, when divided by 4 = 97
Required numbers = 13, 17, 21, …, 97
Let n be the number of terms in this sequence.
Then, nth term = 97
`rArr` a + (n - 1)d = 97
`rArr` 13 + (n - 1)4 = 97
`rArr` (n - 1)4 = 97 - 13 = 84
sequence and Series
`rArr` `(n - 1) = (84)/(4) = 21 rArr n = 22`
`therefore` Sum of all numbers `= S_(22)`
`= (22)/(2)[2 xx 13 + (22 - 1)4]`
` = 11[26 + 84]`
`= 11 xx 110 = 1210`