Question

Find the 4th term of the geometric sequence whose first term is 3 and common ratio is 2.

Answer 1

The 4th term of the geometric sequence whose first term is 3 and the common ratio is 2 is 24.

What is a geometric sequence and how to find its nth terms?

Suppose the initial term of a geometric sequence is a

and the term by which we multiply the previous term to get the next term is r then the sequence would look like

a, ar, ar², ar³,...., arⁿ

Thus, the nth term of such sequence would be aₙ = a₁ × r⁽ⁿ⁻¹⁾ (you can easily predict this formula, as for the nth term, the multiple r would've multiplied with initial terms n-1 times).

Given the first term of the sequence is 3, while the common ratio is 2, therefore, the fourth term of the geometric sequence can be written as,

aₙ = a₁ × r⁽ⁿ⁻¹⁾

a₄ = 3 × 2⁽⁴⁻¹⁾

a₄ = 3 × 2³

a₄ = 24

Hence, the 4th term of the geometric sequence whose first term is 3 and the common ratio is 2 is 24.

Learn more about Geometric Sequence:

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