Find the 12th term of the geometric sequence 1, comma, minus, 4, comma, 16, comma, point, point, .1,−4,16,...
Question
Find the 12th term of the geometric sequence 1, comma, minus, 4, comma, 16, comma, point, point, .1,−4,16,...
Solution
The given sequence is a geometric sequence where each term is multiplied by -4 to get the next term.
The formula for the nth term of a geometric sequence is a * r^(n-1), where:
- a is the first term of the sequence,
- r is the common ratio, and
- n is the term number.
In this case, a = 1, r = -4, and n = 12.
Substituting these values into the formula gives:
1 * (-4)^(12-1) = 1 * (-4)^11
This simplifies to -4^11, which equals -4194304.
So, the 12th term of the sequence is -4194304.
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