Find the 12th term of the geometric sequence 2, comma, minus, 4, comma, 8, comma, point, point, .2,−4,8,...
Question
Find the 12th term of the geometric sequence 2, comma, minus, 4, comma, 8, comma, point, point, .2,−4,8,...
Solution
The given sequence is a geometric sequence where each term is multiplied by -2 to get the next term.
The formula for the nth term of a geometric sequence is:
a_n = a_1 * r^(n-1)
where: a_n is the nth term a_1 is the first term r is the common ratio n is the term number
In this case, a_1 = 2, r = -2, and n = 12.
Substituting these values into the formula gives:
a_12 = 2 * (-2)^(12-1)
a_12 = 2 * (-2)^11
a_12 = 2 * -2048
a_12 = -4096
So, the 12th term of the given geometric sequence is -4096.
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