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Chapter 5: Problem 60

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-4, r=-2\)

Short Answer

Expert verified
The first six terms of the given geometric sequence are -4, 8, -16, 32, -64, 128.

Step by step solution

01

Identify the given values

From the problem, \(a_{1} =-4\) (the first term) and \(r= -2\) (common ratio). These are the known values.
02

Calculate the second term

Using the geometric sequence formula \(a_{n} = a_{1} \cdot r^{(n-1)}\), substitute \(n=2\), \(a_{1}= -4\), and \(r= -2\). The result is \(a_{2} = -4 \cdot (-2)^{(2-1)} = 8\).
03

Calculate the third term

Similarly, for the third term \(n=3\), the result by substituting \(a_{1}=-4\) and \(r=-2\) in the formula is \(a_{3} = -4 \cdot (-2)^{(3-1)} = -16\).
04

Calculate the fourth term

For the fourth term, substituting \(n=4\), \(a_{1}=-4\), and \(r=-2\) into the formula results in \(a_{4} = -4 \cdot (-2)^{(4-1)} = 32\).
05

Calculate the fifth term

Puting \(n=5\), \(a_{1}=-4\), and \(r=-2\) into the formula gives \(a_{5} = -4 \cdot (-2)^{(5-1)} = -64\).
06

Calculate the sixth term

Lastly, for the sixth term, fill in the given values for \(n=6\), \(a_{1}=-4\), and \(r=-2\) in the formula. The final result is \(a_{6} = -4 \cdot (-2)^{(6-1)} = 128\).

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Most popular questions from this chapter

What is an arithmetic sequence? Give an example with your description.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. There's no end to the number of geometric sequences that I can generate whose first term is 5 if I pick nonzero numbers \(r\) and multiply 5 by each value of \(r\) repeatedly.

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{30}\), when \(a_{1}=8000, r=-\frac{1}{2}\).

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(3,8,13,18, \ldots\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If the first term of an arithmetic sequence is 5 and the third term is \(-3\), then the fourth term is \(-7\).
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