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Find the sum of natural numbers and lyin...

Find the sum of natural numbers and lying between 100 and 200 which leave a remainder of 2 when divided by 5 in each case.

A

2990

B

2847

C

2936

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
The natural number which leaves remainder 2 greater than 100 is 102, and less than 200 is 197.
`therefore ` The serires is `102, 107, 112, 117 122, …., 197`.
Number of terms
`" " = (200)/(5) - (100)/(5) = 40 - 20 = 20`.
`S_n = (n)/(2) [a+l] = (20)/(2) [ 102 + 197]`
`" " = (20)/(2) [299] = 2990`.
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