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

Download PDF of This Page (Size: 379K)

Formula of the nth term of an arithmetic sequence

Formula for the Nth Term of an Arithmetic Sequence

Formula of the nth term of an arithmetic sequence

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 .