The given geometric sequence is 4, 16, 64, 256.
What is Geometric Sequence?
- It is defined as the sequence where the ratio between the adjacent numbers is constant.
- It is represented as: G = arⁿ (a = first term; r = common ratio; n = nth term).
Given: Geometric Sequences
Among the given sequences, geometric sequence will be identified if the ration between two adjacent numbers is constant for the given sequence.
Option (A): 5, 12, 17, 29, 46
Common ratio (r) is:
r = 12/5 = 2.4
r = 17/12 = 1.4
r = 29/17 = 1.7
r = 46/29 = 1.6
Here, common ratio is not constant.
Hence, option (A) is incorrect.
Option (B): 3, 7, 11, 15, 19
Common ratio (r) is:
r = 7/3 = 2.3
r = 11/7 = 1.5
r = 15/11 = 1.3
r = 19/15 = 1.3
Here, common ratio is not constant.
Hence, option (B) is incorrect.
Option (C): 4, 6, 10, 16, 26
Common ratio (r) is:
r = 6/4 = 1.5
r = 10/6 = 1.66
r = 16/10 = 1.6
r = 26/16 = 1.62
Here, common ratio is not constant.
Hence, option (C) is incorrect.
Option (D): 4, 16, 64, 256
Common ratio (r) is:
r = 16/4 = 4
r = 64/16 = 4
r = 256/64 = 4
Here, common ratio is constant.
Hence, option (D) is correct.
Therefore, the geometric sequence is 4, 16, 64, 256.
Correct option is (D).
Learn more about the Geometric Sequence here: https://brainly.com/question/14565307
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