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Chapter 8: Problem 11

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, \(a_{1},\) and common ratio, \(r .\) Find \(a_{12}\) when \(a_{1}=5, r=-2\)

Short Answer

Expert verified
So, the 12th term of the geometric sequence (\(a_{12}\)) is -10240.

Step by step solution

01

Identify the known variables

The first term (\(a_{1}\)) is given as 5 and the common ratio (\(r\)) is -2. We are asked to find the 12th term, so \(n=12\).
02

Apply the general formula

We apply the formula \(a_{n} = a_{1} * r^(n-1)\) using the given values. Plugging in the values gives: \(a_{12} = 5 * (-2)^(12-1)\).
03

Solve the calculation

Solve the calculation, remembering that any number to an odd power will keep its sign. \(a_{12} = 5 * (-2)^{11}\) will then become \(a_{12} = 5 * -2048\).
04

Compute the answer

Final step is to multiply 5 by -2048 which gives \(a_{12} = -10240\).

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