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What is the nth term rule of 2,6,18,54?

Published in Sequence Rules 1 min read

The nth term rule of the sequence 2, 6, 18, 54 is 2 * 3(n-1). This sequence is a geometric progression.

Understanding Geometric Progressions

A geometric progression (GP) is a sequence where each term is obtained by multiplying the previous term by a constant value called the common ratio.

Identifying the Pattern

In the sequence 2, 6, 18, 54:

  • The first term (a) is 2.
  • The common ratio (r) can be found by dividing any term by its preceding term. For example, 6 / 2 = 3, 18 / 6 = 3, and 54 / 18 = 3. Therefore, r = 3. As the reference states: to get the next term, multiply the one immediately preceding it by 3.

Deriving the nth Term Rule

The general formula for the nth term of a geometric progression is:

an = a * r(n-1)

Where:

  • an is the nth term
  • a is the first term
  • r is the common ratio
  • n is the term number

Substituting the values from our sequence:

an = 2 * 3(n-1)

Therefore, the nth term rule of the sequence 2, 6, 18, 54 is 2 * 3(n-1).

Examples

Term (n) Calculation Result
1 2 * 3(1-1) 2
2 2 * 3(2-1) 6
3 2 * 3(3-1) 18
4 2 * 3(4-1) 54