The first four terms of a geometric sequence are given by a Subscript 1 Baseline equals 3, a Subscript 2 Baseline equals 12, a Subscript 3 Baseline equals 48,
and a Subscript 4 Baseline equals 192.
Which formula can be used to find a Subscript n Baseline?
Answer options with 5 options
A.
a Subscript n Baseline equals 3 times 4 Superscript n minus 1 Baseline
B.
a Subscript n Baseline equals 3 times 4 Superscript n Baseline
C.
a Subscript n Baseline equals 3 times 9 Superscript n minus 1 Baseline
D.
a Subscript n Baseline equals 9 n plus 3
E.
a Subscript n Baseline equals 9 n minus 6
To find the formula for a Subscript n Baseline in a geometric sequence, we need to observe the pattern in the given terms.
The common ratio, r, can be found by dividing each term by the previous term.
r = a Subscript 2 / a Subscript 1 = 12 / 3 = 4
r = a Subscript 3 / a Subscript 2 = 48 / 12 = 4
r = a Subscript 4 / a Subscript 3 = 192 / 48 = 4
Since the common ratio is consistent, we can use the formula for a geometric sequence:
a Subscript n Baseline = a Subscript 1 * r^(n-1)
In this case, a Subscript 1 = 3 and r = 4, so the formula is:
a Subscript n Baseline = 3 * 4^(n-1)
The correct answer is:
A. a Subscript n Baseline = 3 times 4 Superscript n minus 1 Baseline