Consider the sequence⟨8,4,2,1,0.5,……⟩⟨8,4,2,1,0.5,……⟩. Find the12th12thterm of the sequence.Select one:A.12451245B.12651265C.12561256D.1266
Question
Consider the sequence ⟨8, 4, 2, 1, 0.5,……⟩. Find the 12th term of the sequence.
Select one:
- A. 1245
- B. 1265
- C. 1256
- D. 1266
Solution
The given sequence is a geometric sequence where each term is half of the previous term. The general formula for the nth term of a geometric sequence is a*r^(n-1), where a is the first term, r is the common ratio, and n is the term number.
In this case, a = 8 (the first term), r = 0.5 (each term is half of the previous term), and n = 12 (we're looking for the 12th term).
So, the 12th term is 8*(0.5)^(12-1) = 8*(0.5)^11.
Calculating this gives approximately 0.00390625.
So, none of the options A, B, C, or D are correct.
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