NCERT Class 11 Mathematics Solutions: Chapter 9 – Sequences and Series Miscellaneous Exercise 9 Part 17 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Formula for the Nth Term of an Arithmetic Sequence

1. A manufacturer reckons that the value of a machine, which costs him , will depreciate each year by . Find the estimated value at the end of years.


Cost of machine

Machine depreciates by every year.

Its value after every year is of the original cost

of the original cost.

Value at the end of

The value of the machine at the end of years is .

2. workers were engaged to finish a job in a certain number of days. workers dropped out on second day, more workers dropped out on third day and so on. It took more days to finish the work. Find the number of days in which the work was completed.


Consider be the number of days in which workers finish the work.

According to the given information,

The series terms is an A. P. with first term , common difference and number of terms as

So, cannot be negative.

Originally, the number of days in which the work was completed is .

Required number of days