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Question

The sum of the integers from 1 to 100 which are divisible by 3 and 5, is


A

2317

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B

2632

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C

315

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D

2489

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Solution

The correct option is C

315


Explanation for the correct option:

Step 1: Form the required AP

LCM of 3 and 5=15 why did you calculate the LCM? explain

So, the terms divisible by 15 which lie between 1 to 100 are part of A.P. how? explain

A.P.=15,30,45,......,90

Step 2: Find the sum of the AP

A.P.=15,30,45,......,90

a=15d=15an=a+(n-1)d90=15+(n-1)15n=6 what is a, d an and n? define.

Sum of the A.P, Sn=n22a+(n-1)d

S6=62(2(15)+(6-1)15)S6=3(30+75)S6=315

Hence, the correct option is C.


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