A geometric progression has a first term of 5 and a common ratio of 2. What is the 6^{\tex… — JAMB UTME

A geometric progression has a first term of $5$ and a common ratio of $2$ . What is the $6^{\text{th}}$ term of this progression?

The

6^{\text{th}}

term of the geometric progression is

160

The

n^{\text{th}}

term of a geometric progression is given by

T_n = a r^{n-1}

. Substituting

a = 5

r = 2

, and

n = 6

yields

T_6 = 5 \times 2^5 = 5 \times 32 = 160

, which makes

160

the correct value.

Identify the given values from the problem statement.

First term

a = 5

, common ratio

r = 2

, and term index

n = 6

These parameters are required for the

n^{\text{th}}

term formula of a geometric progression.

State the formula for the

n^{\text{th}}

term of a Geometric Progression (GP).

T_n = a r^{n-1}

The

n^{\text{th}}

term of a GP is obtained by multiplying the initial term by the common ratio raised to the power of

n-1

Substitute the values into the formula and evaluate.

T_6 = 5 \times 2^{6-1} = 5 \times 2^5 = 5 \times 32 = 160

Evaluating

2^5 = 32

and then multiplying by

5

yields the correct

6^{\text{th}}

term.

Geometric Progression

n^{\text{th}}

Term

Question