NCERT Class 11 Mathematics Solutions: Chapter 9 –Sequences and Series Miscellaneous Exercise 9 Part 2

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In figure formula of arithmatic series is shown.

Formula of Arithmetic Series

In figure formula of arithmatic series is shown.

1. Let the sum of terms of an A.P. be , respectively, show that

Answer:

Consider be the first term and the common difference of the A.P. respectively.

So,

From eq (1) and (2)

So, the given result is proved.

2. Find the sum of all numbers between which are divisible by .

Answer:

The numbers lying between , which are divisible by , are

First term, Last term,

Common difference,

Consider the number of terms of the A.P. be n.

So, the required sum is .