Question

If the third term in a geometric sequence is 20, and the fifth term in the
sequence is 5, what is the ratio (multiplier)?

A) 1/2
B) 1/4
C) 2
D) 1/16​

Answer 1

Answer: A) 1/2

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.

If the third term is 20, it means that

T3 = 20 = ar^(3 - 1)

20 = ar²- - - - - - - - - - 1

If the third term is 20, it means that

T5 = 5 = ar^(5 - 1)

5 = ar⁴- - - - - - - - - - 2

Dividing equation 2 by equation 1, it becomes

5/20 = r⁴/r²

1/4 = r^(4 - 2)

(1/2)² = r²

r = 1/2