Geometric sequences and series

Question 1

What is a geometric sequence?

Answer 1

A sequence in which each term is found by multiplying the previous term by a fixed constant

Question 2

What is the common ratio of a geometric sequence?

Answer 2

The constant that each term is multiplied by to give the next

Question 3

Given the first term (a) and the common ratio (r) of a geometric sequence, how can Uⁿ be calculated?

Answer 3

arⁿ⁻¹

Question 4

Given the first term (a) and the common ratio (r) of a geometric sequence, how can Sⁿ be calculated?

Answer 4

a(1-rⁿ)/(1-r)

Question 5

What is a convergent series?

Answer 5

A series that approaches a finite value as more terms are added

Question 6

When is a geometric series convergent?

Answer 6

When |r|<1, where r is the common ratio

Question 7

Given the first term (a) and the common ratio (r) of a convergent geometric sequence, how can the sum to infinity of the series be calculated?

Answer 7

a/(1-r)