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Find the 12th term of the geometric sequence 2, -8, 32, ...

User HAdes
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Answer:

The 12th term of the geometric sequence 2, -8, 32, ... is -8,388,608.

Explanation:

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant factor. In this case, the constant factor can be found by dividing any term by the previous term:

-8 / 2 = -4

32 / -8 = -4

So the constant factor, or the common ratio (r), is -4.

The general formula for finding the nth term of a geometric sequence is:

an = a1 * r^(n-1)

where an is the nth term, a1 is the first term, r is the common ratio, and n is the position of the term in the sequence.

We want to find the 12th term (a12), so n = 12. The first term (a1) is 2, and the common ratio (r) is -4:

a12 = 2 * (-4)^(12-1)

a12 = 2 * (-4)^11

Now calculate the value:

a12 = 2 * (-4194304)

a12 = -8388608

User Ben Wilson
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