Verified Answer :

olemakpadu

For Geometric,  \(T_{n}\) =  arⁿ⁻¹

T₂ = ar²⁻¹ = ar¹ = 12...........(a)

T₄ = ar⁴⁻¹ = ar³ = 4/3..........(b)

Equation (b) / (a)

ar³ / ar = 4/3 ÷ 12

r² = 1/9

r = √(1/9)

r = 1/3

Common ratio, r = 1/3.

MrRoyal

The common ratio of the geometric sequence is 1/3

How to determine the common ratio?

The terms are given as:

T2 = 12

T4 = 4/3

The nth term of a geometric sequence is calculated using

Tn = ar^(n-1)

So, we have:

T2 = ar

T4 = ar^3

Divide T4 by T2

\(\frac{T4}{T2} = \frac{ar^3}{ar}\)

Divide

\(\frac{T4}{T2} = r^2\)

Substitute T2 = 12 and T4 = 4/3

\(\frac{4/3}{12} = r^2\)

Divide

\(\frac{4}{36} = r^2\)

Take the square roots

\(r = \frac 26\)

Simplify

\(r = \frac 13\)

Hence, the common ratio is 1/3

Read more about geometric sequence at:

https://brainly.com/question/24643676

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