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3 years ago

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36, _, _, 32/3 is a geometric sequence, with some terms missing. First, please solve for "r", the common ratio between each

term. What is the value of r?

1 answer:

Ksju [112]3 years ago

3 0

Answer: r = 2/3

Step-by-step explanation:

In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = 36

The 4th term is 32/3

n = 4

Therefore,

T4 = 32/3 = 36 × r^(4 - 1)

32/3 = 36 × r^3

Dividing both sides if the equation by 36, it becomes

32/3 × 1/36 = r^3

8/27 = r^3

Taking cube root of both sides of the equation, it becomes

(8/27)^1/3 = r^3 × 1/3

r = 2/3

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