Problem 8
Question
Write the first five terms of each geometric sequence. $$a_{n}=-6 a_{n-1}, \quad a_{1}=-2$$
Step-by-Step Solution
Verified Answer
The first five terms of the sequence are: -2, 12, -72, 432, -2592.
1Step 1: Calculate the First Term, \(a_{1}\)
This is the provided starting point of the sequence, and no calculations are necessary. The first term, \(a_{1}\), is -2.
2Step 2: Calculate the Second Term, \(a_{2}\)
The second term can be calculated by multiplying the preceding term (\(a_{1}\)) by the common ratio: \(a_{2}= -6*a_{1} = 12\).
3Step 3: Calculate the Third Term, \(a_{3}\)
The third term is obtained in the same manner: it is the second term multiplied by the common ratio: \(a_{3}= -6*a_{2} = -72\).
4Step 4: Calculate the Fourth Term, \(a_{4}\)
The fourth term is calculated in the same way: it's the third term multiplied by the common ratio: \(a_{4}= -6*a_{3} = 432\).
5Step 5: Calculate the Fifth Term, \(a_{5}\)
Finally, the fifth term is the fourth term multiplied by the common ratio: \(a_{5}= -6*a_{4} = -2592\).
Other exercises in this chapter
Problem 7
In Exercises \(1-14\), write the first six terms of cach arithmetic sequence $$a_{1}=\frac{s}{2}, d=-\frac{1}{2}$$
View solution Problem 8
Use the formula for \(_{n} P_{t}\) to evaluate each expression. $$ _{6} P_{0} $$
View solution Problem 8
Write the first four terms of each sequence whose general term is given. $$a_{n}-(-1)^{n+1}(n+4)$$
View solution Problem 9
In Exercises 9-30, use the Binomial Theorem to expand each binomial and express the result in simplified form. $$(x+2)^{3}$$
View solution