NCERT Class 11-Math՚s: Chapter – 9 Sequence and Series Part 8 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Question 4:

If the and terms of a G. P. are and respectively, show that its term is .

Answer:

The term of GP is given by where a is the first term and is the common difference

term is given as

term is given as p

Using (a) and (b)

term is given by

But and the term is

But

Hence proved the term is

Question 5:

A carpenter was hired to build window frames. The first day he made five frames and each day, thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?

Answer:

The first day he made frames then two frames more than the previous that is then and so on

Hence the sequence of making frames each day is

The sequence is AP with first term as and common difference

Total number of frames to be made is

Let is requires days hence

The sum of first terms of AP is given by

Where a is the first term and d is common difference

and

But n represents number of days which cannot be negative hence

Hence number of days required to finish the job is days.