NCERT Class 11-Math's: Chapter –9 Sequence and Series Part 7

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Question 2:

A man saved in years. In each succeeding year after the first year he saved more than what he saved in the previous year. How much did he save in the first year?

Answer:

The total amount saved in years is hence

Let the amount saved in first year be ‘a’

Then as he increases every year then the amount in second year will be ‘’ then in third year ‘’ and so on

The sequence will be a,

The sequence is AP and the common difference is

There are terms in the sequence as he saved money for years

Using the sum formula for AP

Where n is number of terms a is the first term and d is the common difference

Given that

Hence amount saved in first year is Rs.

Question 3:

A man accepts a position with an initial salary of per month. It is understood that he will receive an automatic increase of in the very next month and each month thereafter.

(a) Find his salary for the tenth month

(b) What is his total earnings during the first year?

Answer

His salary in first month is and then it increases every month by

Hence the sequence of his salary per month will be

The sequence is in AP with first term as , common difference as

(a) We have to find salary in 10th month that is 10th term of the AP the nth term of AP is given by

Where a is the first term and d is the common difference

We have to find

Hence salary in 10th month is

(b) To get the total earnings in first year we have to add first terms of the sequence that is we have to find

The sum of first terms of AP is given by

Where a is the first term and d is common difference

Hence his total earnings in first year is

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