Find the values of s1 and r for a geometric sequence with s4 = 18 and s6= 72

option b is the correct answer.

Step-by-step explanation:

In a geometric series, the successive terms differ by a common ratio which is determined by dividing a term by the preceding term.

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 between successive terms in the sequence.

n represents the number of terms in the sequence.

The formula representing the 4th term of the given sequence would be expressed as

18 = a × r^(4 - 1)

18 = ar^3- - - - - - - - - - - - - - - -1

The formula representing the 6th term of the given sequence would be expressed as

72 = a × r^(6 - 1)

72 = ar^5- - - - - - - - - - - - - - - -2

Dividing equation 2 by equation 1, it becomes

4 = r^(5 - 3)

2² = r^2

r = 2

Substituting r = 2 into equation 1, it becomes

18 = a × 2^3

18 = 8a

a = 18/8 = 2.25

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