Free Printable Infinite Sequences

1.

Does this sequence converge or diverge? $\left\{\frac{10n-6}{2n-3}\right\}$

a)

Converges to 0

b)

Converges to 2

c)

Converges to 5

d)

Diverges

2.

Does this sequence converge or diverge? $\frac{1}{4},\frac{1}{9},\frac{1}{16},\frac{1}{25},...$

a)

Converges to 0

b)

Converges to 1

c)

Converges to 5

d)

Diverges

3.

Which of the following expresses 1+3+5+...+39

a)

$\sum_{k=1}^{20}2k-1$

b)

$\sum_{k=2}^{40}k-1$

c)

$\sum_{k=-1}^{37}k+2$

d)

$\sum_{k=1}^{39}2k-1$

4.

What is the sum of this series?

a)

75/4

b)

100

c)

25/4

d)

∞ (the series diverges)

5.

The n^th term of a geometric sequence is given by ...

a)

b)

c)

d)

6.

Evaluate the 5^th partial sum of the given geometric sequence: 2 , 12 , 72 , ...

a)

3110

b)

2592

c)

18,662

d)

cannot be determined

7.

Does the series converge or diverge ?

a)

Converge

b)

Diverge

c)

Cannot be determined

8.

Determine the common ratio, r , for the given geometric sequence.

a)

-1/2

b)

1/2

c)

-2/3

d)

-1/4

9.

What will this formula tell us?

a)

The partial sum of a geometric series.

b)

The common ratio of a geometric series.

c)

The sum of a convergent geometric series.

d)

The number of terms in a partial geometric series.

10.

What series is this?

a)

P-series.

b)

Geometric series.

c)

Harmonic series.

d)

Alternating harmonic series.

11.

The infinite series is...

a)

harmonic

b)

a p-series

c)

geometric

d)

a Taylor

12.

Which of the following tests would be the best choice to prove the series is divergent?

a)

nth term test

b)

integral test

c)

direct comparison test

d)

limit comparison test

13.

a₁
S_n = ------------------
1 - r
What formula is this?

a)

Infinite Arithmetic Series Formula

b)

Finite Geometric Series Formula

c)

Finite Arithmetic Series Formula

d)

Infinite Geometric Series Formula

14.

On which of the following series could a FINITE infinite sum be found?

a)

1 + 3 + 6 + 10 + ...

b)

3 + 6 + 12 + 24 + ...

c)

10 + 5 + 0 + -5 + ...

d)

64 + 32 + 16 + 8 + ...

15.

What is the explicit rule for the sequence:
11, 22, 44, 88...

a)

g_n = 2(11)^n-1

b)

g_n = 11x2

c)

g_n = 11(2)^n-1

d)

g_n = 11+(2)^n-1

Infinite Sequences

Total questions: 15

Worksheet time: 23mins

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