The first term of a geometric progression (GP) is 2 and its common ratio is 3. What is the… — JAMB UTME

The first term of a geometric progression (GP) is $2$ and its common ratio is $3$ . What is the $4^{\text{th}}$ term of the progression?

The

4^{\text{th}}

term of the geometric progression is

54

For a geometric progression with first term

a

and common ratio

r

, the

n^{\text{th}}

term is given by

T_n = a r^{n-1}

. Substituting

a = 2

r = 3

, and

n = 4

yields

T_4 = 2 \times 3^3 = 2 \times 27 = 54

Identify the given parameters of the geometric progression.

First term

a = 2

, common ratio

r = 3

, and term position

n = 4

These values are directly provided in the question statement.

Apply the general formula for the

n^{\text{th}}

term of a geometric progression,

T_n = a r^{n-1}

T_4 = 2 \times 3^{4-1} = 2 \times 3^3

The exponent of the common ratio is always one less than the term index

n

Evaluate the exponent and multiply by the first term.

3^3 = 27

, so

T_4 = 2 \times 27 = 54

Performing standard arithmetic yields the exact term value.

Formula for the nth term of a Geometric Progression:

T_n = a r^{n-1}

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