Question

1- What is a geometric progression? Give an example to justify your answer.

Answer 1

* As HOMEWORKLIB.com answering guidelines, only 4 parts of the question are being answered. Since it is not specified, which 4 to answer, so we are solving the first 4 parts.

Ans. 1.

In a geometric progression, the ratio between consecutive terms is same. For example, the given series:

2,6,18,54...

Here the ratio 6/2 is same as 18/6 is equal to 3. So, the common ratio is 3.

Ans. 2.

In an Arithmetic Progression, the difference between consecutive terms is same. For example, the given series:

2,5,8,11,14...

Here the difference 5-2 = 8-5 = 3 ans so on. So, the common difference is 3.

Ans. 3.

The recurrence relation is an equation, in which the nth term of the sequence is defined in terms of other terms in the relation. There is always a base condition defined, otherwise we cannot solve the recurrence relation.

Example:

Tn = Tn-1 + Tn-2

Base condition is T0 = 0, T1 = 1.

The series generated is 0,1,1,2,3,5,8,13...

This is a popular Fibonacci series.

Ans. 4.

The recurrence relation can be solved using these methods:

1. Substitution method.

2. Recurrence tree method.