## Unit 04: Sequence and Series (Solutions)

This is a forth unit of the book Mathematics 11 published by Khyber Pakhtunkhwa Textbook Board, Peshawar, Pakistan. On this page we have provided the solutions of the questions.

After reading this unit the students will be able to

- Define a sequence (progression) and its terms.
- Know that a sequence can be constructed from a formula or an inductive definition.
- Recognize triangle, factorial and pascal sequences.
- Define an arithmetic sequence.
- Find the nth or general term of an arithmetic sequence.
- Solve problems involving arithmetic sequence.
- Know arithmetic mean between two
- Insert n arithmetic means tEtween two numtErs.
- Define an arithmetic series.
- Establish the formula to find the sum to n terms of an arithmetic series.
- Show that sum of $n$ arithmetic means between two numbers is equal to n times their arithmetic mean.
- Solve real life problems involving arithmetic series.
- Define a geometric sequence.
- Find the $n$th or general term of a geometric sequence.
- Solve problems involving geometric sequence.
- Know geometric mean between two numbers.
- Insert $n$ geometric means between two numbers.
- Define a geometric series.
- Find the sum of $n$ terms of a geometric series.
- Find the sum of an infinite geometric series.
- Convert the recurring decimal into an equivalent common fraction.
- Solve real life problems involving geometric series.
- Recognize a harmonic sequence.
- Find $n$th term of harmonic sequence.