A geometric sequence has the first term a1 = −3 and common ratio r = 1/2 . What is the 8th term?

Expert Solution

Consider a geometric sequence with first term a1 = -3 and common ratio r = 1/2

Use the formula for nth term of a geometric sequence,,

an = a1 ∙ rn-1 ...... (1)

Substitute a1 = -3, r = 1/2 and n = 8 in the formula (1) and compute 8th term of given sequence,

a8= -3 × (1/2)8-1

= -3 × 1/128

= -3/128

Therefore, 8th term of given sequence is a3 = -3/128.

Junaid answered 1 year ago

For the following exercises, write the first five terms of the geometric sequence, given the first term and common ratio. a1 = 5, r = 1/5

What are the first five terms of the geometric sequence a1 = 3, an = 4 ⋅ an − 1 ?

What are the first five terms of the geometric sequence a1 = 3, an = 4 ⋅ an − 1?

An arithmetic sequence has the first term a1 = 18 and common difference d = −8. What are the first five terms?

How is the common ratio of a geometric sequence found?

For the following exercises, find the common ratio for the geometric sequence.

What is the 11th term of the geometric sequence − 1.5, − 3, − 6, − 12, … ?

Find the common ratio for the geometric sequence 2.5, 5, 10, 20, …

Given the geometric sequence an = 4n . Find the first three terms and the common...

Given the geometric sequence an = 4n . Find the first three terms and the common ratio.

Define a sequence from R as follows. Fix r > 1. Let a1 = 1 and...

Define a sequence from R as follows. Fix r > 1. Let a1 = 1 and define recursively, an+1 = (1/r) (an + r + 1). Show, by induction, that (an) is increasing and bounded above by (r+1)/(r−1) . Does the sequence converge?

If the first term is 10 and the common ratio of a GP is 3, then write the first five terms of GP.

Question