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NCERT Class 11- Math՚s: Chapter – 9 Sequence and Series Part 8
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.