NCERT Class 11 Mathematics Solutions: Chapter 9 –Sequences and Series Miscellaneous Exercise 9 Part 3
Glide to success with Doorsteptutor material for IEO : fully solved questions with step-by-step explanation- practice your way to success.
Formula for 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 .