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Chapter 5: Problem 55

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=10, r=-4\)

Short Answer

Expert verified
The first six terms of the geometric sequence are 10, -40, 160, -640, 2560, -10240.

Step by step solution

01

Find the first term

The first term of the sequence is the given \(a_{1} = 10\).
02

Find the second term

The second term \(a_{2}\) can be found by multiplying the first term by the common ratio: \(a_{2} = a_{1} \times r = 10 \times -4 = -40\).
03

Find the third term

The third term \(a_{3}\) can be found by multiplying the second term by the common ratio: \(a_{3} = a_{2} \times r = -40 \times -4 = 160\).
04

Find the fourth term

The fourth term \(a_{4}\) can be found by multiplying the third term by the common ratio: \(a_{4} = a_{3} \times r = 160 \times -4 = -640\).
05

Find the fifth term

The fifth term \(a_{5}\) can be found by multiplying the fourth term by the common ratio: \(a_{5} = a_{4} \times r = -640 \times -4 = 2560\).
06

Find the sixth term

The sixth term \(a_{6}\) can be found by multiplying the fifth term by the common ratio: \(a_{6} = a_{5} \times r = 2560 \times -4 = -10240\).

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Most popular questions from this chapter

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(\frac{1}{2}, 1, \frac{3}{2}, 2, \ldots\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(7,-7,-21,-35, \ldots\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{4}\), when \(a_{1}=4, r=-3\).

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{40}\), when \(a_{1}=6, r=-1\).

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I've noticed that the big difference between arithmetic and geometric sequences is that arithmetic sequences are based on addition and geometric sequences are based on multiplication.
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