# NCERT Class 11 Mathematics Solutions: Chapter 9 –Sequences and Series Miscellaneous Exercise 9 Part 3

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1. Find the sum of integers from that are divisible by .

Answer:

The integers from , which are divisible by , are .

This forms an A.P. with both the first term and common difference equal to .

The integers from , which are divisible by, are .

This forms an A.P. with both the first term and common difference equal to 5.

Required sum

So, the sum of the integers from , which are divisible by , is

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

Answer:

The two-digit numbers, which when divided by , yield as remainder, are 13, 17, … 97.

This series forms an A.P. with first term and common difference 4. Let n be the number of terms of the A.P.

It is known that the nth term of an A.P. is given by,

Sum of n terms of an A.P. is given by

So, the required sum is .