IM 3 Sequences and Series

Vocabulary

300

What is the difference between an arithmetic and a geometric sequence?

An arithmetic sequence is a sequence that has a common difference (the same number gets added each time).

A geometric sequence is a sequence that has a common ratio (the same number gets multiplied each time).

500

What is the difference between a sequence and a series?

A sequence is an ordered list of numbers, whereas a series is the sum of a given number of terms in a sequence.

Arithmetic, Geometric, or Neither?

100

Arithmetic, Geometric or Neither? State the common difference or common ratio if there is one.

5, 10, 15, 20,...

Arithmetic

d = 5

200

Arithmetic, Geometric or Neither? State the common difference or common ratio if there is one.

2, 10, 50, 250,...

Geometric

r = 5

300

Arithmetic, Geometric or Neither? State the common difference or common ratio if there is one.

-1, 4, 10, 17, 25,...

Neither

400

Arithmetic, Geometric or Neither? State the common difference or common ratio if there is one.

-16, -12, -8, -4,...

Arithmetic

d = 4

500

Arithmetic, Geometric or Neither? State the common difference or common ratio if there is one.

−2.5, 10, −40, 160, −640

Geometric 

d = -4

Arithmetic Sequences

100

Find the common difference, then state the rule. 

-2, 2, 6, 10, 14, ...

d = 4

a_n = 4(n-1) - 2

200

For the given sequence, find the common difference and the 10th term.

9, 12, 15, 18, ...

d = 3

a₁₀ = 36

300

For the given sequence, find the common difference and the 15th term.

−3, −23, −43, −63, ...

d = -20

a₁₅ = -283

400

Given that a₁ = 7 and the common difference is -2, find a₆

a₆ = -3

500

For the given sequence, find the common difference and the 15th term.

−34, −64, −94, −124, ...

d = -30 

a₁₅ = -454

Geometric Sequences

100

For the given sequence, find the common ratio

1/2, 2, 8, 32, ...

r = 4

200

For the given geometric sequence, find the common ratio:

125, 25, 5, 1,...

r = 1/5

300

Given that a₁ = 3 and r = 2, find a₆.

a₆ = 96

400

Write the formula for the given geometric sequence:

32, 16, 8, 4, ...

a_n = 32 (1/2) ^n-1

500

For the given geometric sequence, find the common ratio and then find the 8th term.

−1, 6, −36, 216, ...

r = -6

a₈ = 279,936

Arithmetic and Geometric Series

100

Find the sum of the arithmetic sequence given:

a₁ = 4, a₁₀ = 22, n = 10

S₁₀ = 130

200

Find the sum of the geometric sequence given:

2 + 8 + 32 + 128 ...    n = 8

S_n = 43690 

300

Find the sum of the arithmetic sequence given:

20 + 30 + 40 + 50..., n = 15

S_n = 1350 

400

Find the sum of the geometric sequence given:

-3 + 15 - 75 + 375 ...    n = 8

S_n= 195312

500

Find the sum of the arithmetic sequence given:

20 + 27 + 34 + 41..., n = 16 

S₁₆ = 1160