The 3^{\text{rd}} term of a geometric progression (G.P.) is 18 and its common ratio is 3. … — JAMB UTME

The $3^{\text{rd}}$ term of a geometric progression (G.P.) is $18$ and its common ratio is $3$ . What is the first term of the progression?

Answer: 2

The first term of the geometric progression is 2.

In a geometric progression, the

n^{\text{th}}

term is given by

T_n = a r^{n-1}

. For the

3^{\text{rd}}

term (

n = 3

) with common ratio

r = 3

and term value

18

, the equation is

18 = a \cdot 3^{2} = 9a

. Dividing by

9

yields the first term

a = 2

Identify the formula for the

n^{\text{th}}

term of a geometric progression.

T_n = a r^{n-1}

This formula connects the

n^{\text{th}}

term

T_n

to the first term

a

, common ratio

r

, and term index

n

Substitute

T_3 = 18

r = 3

, and

n = 3

into the formula.

18 = a \cdot 3^{3-1} \implies 18 = 9a

Evaluating

3^{3-1} = 3^2 = 9

simplifies the equation.

Solve for the first term

a

a = \frac{18}{9} = 2

Dividing both sides of the equation by 9 isolates the first term.

Geometric Progression nth term calculation

Question