How To Find The Ratio Of A Geometric Sequence

Common Ratio Formula

Before learning the common ratio formula, allow us call back what is the mutual ratio. The number multiplied (or divided) at each stage of a geometric sequence is called the "common ratio", because if yous divide (that is, if y'all find the ratio of) successive terms, y'all'll ever become this value. The common ratio formula helps in computing the common ratio for a given geometric progression.

What Is the Common Ratio Formula?

The general grade of representing a geometric progression is a_i, (a₁r), (a₁r²), (a_aner³), (a_aner⁴) ,... where a₁ is the get-go term of GP, a₁r is the 2nd term of GP, and r is the common ratio. Thus, the common ratio formula of a geometric progression is given as,

Mutual Ratio Formula:

Common ratio, \(r = \frac{a_n}{a_{due north-1}}\)

where,

• a\(_n\) is the n^thterm of the geometric progression.
• a\(_{northward-one}\) is the (n - 1)^thterm of the geometric progression.

Permit u.s. see the applications of the common ratio formula in the following department.

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Examples Using Common Ratio Formula

Example ane: Find the common ratio for the geometric sequence 1, 2, 4, 8, sixteen,... using the common ratio formula.

Solution:

To observe: Common ratio

Dissever each term by the previous term to determine whether a mutual ratio exists.

\(\frac{2}{1} = \frac{4}{2} = \frac{8}{4} = \frac{16}{8} = two \)

The sequence is geometric because in that location is a mutual multiple, two, which is called the common ratio.

Answer:  Common ratio, r = 2

Case ii:What is the common ratio for a geometric sequence whose formula for the n ^thursday term is given past: a\(_n\) = iv(3)^{due north-one}?

Solution:

To discover: Common ratio

Given: Formula of geometric sequence = 4(three)^{due north-one}

A list of the terms volition show what is happening in the sequence (start with n = 1).

4, 12, 36,108,...

Using the mutual ratio formula,

r = 12/4 = 3

Answer:  Common ratio, r = three

Source: https://www.cuemath.com/common-ratio-formula/

Posted by: mcdonaldhiseetter.blogspot.com

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