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Chapter 8: Problem 7

Write the first five terms of each geometric sequence. $$a_{n}=-5 a_{n-1}, \quad a_{1}=-6$$

Short Answer

Expert verified
The first five terms of the sequence are -6, 30, -150, 750, -3750.

Step by step solution

01

Identify the first term

The first term of the sequence is provided as \(a_{1} = -6\).
02

Apply the formula for the second term

The formula provided is \(a_{n} = -5 \times a_{n-1}\). Here, for \(n=2\), the formula becomes \(a_{2} = -5 \times a_{1}\). Substitute the value of \(a_{1} = -6\) into the formula to find \(a_{2} = -5 \times -6 = 30\).
03

Apply the formula for the third term

For \(n=3\), the formula changes to \(a_{3} = -5 \times a_{2}\). Substituting the value of \(a_{2} = 30\) into the formula, we get \(a_{3} = -5 \times 30 = -150\).
04

Apply the formula for the fourth term

For \(n=4\), the formula changes to \(a_{4} = -5 \times a_{3}\). Substitute \(a_{3} = -150\) into the formula to get \(a_{4} = -5 \times -150 = 750\).
05

Apply the formula for the fifth term

For \(n=5\), the formula becomes \(a_{5} = -5 \times a_{4}\). Substituting the value of \(a_{4} = 750\) into the formula, we get \(a_{5} = -5 \times 750 = -3750\).

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