Geometric Sequences & Series & Mathematics of Finance Quiz

Given the nth term of a sequence a_n = 5(2)^n-1, what is the first term of the sequence?

• 5

• 10

• 2.5

• 2

For the sequence where the nth term is given by a_n = 3(-4)^n-1, what is the common ratio r?

• 3

• -4

• 12

• -12

If the nth term of a geometric sequence is a_n = (5/2)(-1/2)^n-1, what is the fourth term of the sequence?

• -5/16

• -5/8

• 5/8

• 5/16

For the geometric sequence with the first term a₁ = √3 and common ratio r = √3, what is the fourth term?

• 3

• 9

• √3

• 3 √3

Looking at the sequence 2, 4, 8, 16, ..., determine whether it is geometric and if so, find the common ratio.

• Not geometric

• Geometric, r = 2

• Geometric, r = 4

• Geometric, r = 8

Is the sequence 1, 1, 1, 1.21, 1.331, ... geometric? If yes, what is the common ratio?

• Yes, r = 1.1

• No, it is not geometric

• Yes, r = 1.01

• Yes, r = 1.21

Determine the n^th term of the geometric sequence:

7, 14/3, 28/9, 56/27, ...

• a_n = 7(2/3)^n-1

• a_n = 7(2)^n-1

• a_n = (2/3)(7)^n-1

• a_n = 7(3/2)^n-1

Find the partial sum S_n of the geometric seqeuence that satisfies the given conditions:

a₁ = 5, r = 2, n = 5

• 155

• 150

• 129

• 45

Find the sum:

• 4655

• 4655/32

• 32

• Not Possible

Determine whether the infinite geometric series is convergent or divergent. If it is convergent, find its sum.

1 + 1/3 + 1/9 + 1/27

• Divergent

• Convergent, S = 3/2

• Convergent, r = 1/3