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Algebra

Geometric Sequence

Formula
aₙ = a₁ × rⁿ⁻¹

What is Geometric Sequence?

A geometric sequence is a sequence where each term is found by multiplying the previous term by a constant ratio r. The nth term is the first term times the common ratio raised to the (n−1) power.

Variables

  • a
    aₙ — nth term
  • a
    a₁ — First term
  • r
    r — Common ratio
  • n
    n — Term number

Worked Examples

Example 1

Find the 5th term of the sequence 2, 6, 18, 54, ...

Solution:

a₁ = 2, r = 3. a₅ = 2 × 3⁴ = 2 × 81 = 162

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