GCSE Geometric Sequences Questions and Answers

1. What is a Geometric Sequence?

A geometric sequence is a sequence of numbers in which each term is found by multiplying or dividing the previous term by a fixed, non-zero number called the common ratio. 

Here are a few examples of a geometric sequence,

5, 10, 15, 20, 25, 30,....  (Next term = Multiply by 5 the previous term)

32, 16, 8, 4, 2, 1,....  (Next term = Divide by 2 the previous term)

2. Types of Geometric Sequences:

There are two types of geometric sequences: increasing and decreasing geometric sequences.

2.1  Increasing Geometric Sequences:

• Each successive term is larger than the one before it.
• Common ratio must be positive.
• Example: 4, 8, 16, 32, 64,........

2.2  Decreasing Geometric Sequences:

• Each successive term is smaller than the one before it.
• Common ratio must be negative.
• Example: 81, 27, 9, 3, 1……

3. Geometric Sequence Formula:

The geometric sequence formula is a_n= a(r)^{n - 1}

Where,

a_n is the n^th term

a is the first term

n is the term position

r is the common ratio.

Any geometric sequence has the following terms: 

a, ar, ar², ar³…. Where a is the first term and r is the common ratio.

3.1 How to Find a Common Ratio?

It is a ratio of two consecutive numbers in any geometric sequence. It is calculated as follows,

3.2 How to Find Next Terms for Geometric Sequences?

To find the next term of any geometric sequence these are the steps need to follow:

Step 1: Choose any two consecutive terms from the given sequence

Step 2: Divide the second term by the first term to get the value of the common ratio.

Step 3: Multiply the previous term by the common ratio to get the next term.

4. N^th Term for Geometric Sequence:

To find N^th term of a given geometric sequence steps need to follow:

Step 1: Choose any two consecutive terms of the given sequence.

Step 2: Find the common ratio.

Step 3: Substitute values of 

a and r  in geometric sequence formula,  a_n= a(r)^{n - 1}

Step 4: Find the N^th  term by substituting the value of n.

Let’s learn how to calculate the successive terms or missing terms for the given geometric sequence in the following examples.

Let’s learn how to calculate the nth formula or nth term for the given geometric sequence in the following examples.