Sequences and Series

Arithmetic Sequence

100

What is the common difference in 

3, 11, 19, 27, 35, ...? 

What is the 6th term?

d=8, 6th term=43

200

Determine the value of n for the given sequence:

-19, -13, -7,..., 119

n=24

300

Determine the first term of the arithmetic sequence in which the 16th term is 110 and the common difference is 7.

5

400

Find the first five terms of the sequence an=10-2n

8, 6, 4, 2, 0

500

The first term of an arithmetic sequence is 5y and the common difference is -3y.

What is a₁₅ of the sequence?

a₁₅=-37y

Arithmetic Mean and Series

100

Find S₁₀ for the following series, 

10+7+4+...

S₁₀=-35

200

Determine S₃₀ for the following series:

5 + 5.3 + 5.6 +...

S₃₀=280.5

300

The 79th partial sum of the series 32+43+54+...

36,419

400

A hardware store makes a profit of 30,000 dollars during its first year. The store owner sets a goal of increasing profits by 5,000 dollars each year for 4 years. Assuming that this goal is met, find the total profit during the first 5 years of business.

200,000 dollars 

500

The sum of the series 45+60+75+...+405.

5,625

Geometric Sequence

100

Given the sequence: 400, 320, 256, ... Find a₆.

131.072

200

Determine the formula for the nth term of the geometric sequence:

192, -48, 12, -3,...

a_n=192(-1/4)^n-1

^{a_n=192(-0.25)n-1}

300

Given the sequence: 400, 200, 100, ... Find a₉

1.5625

400

Given the geometric sequence: -1, -4, -16... Find a₁₀

-262,144

500

A ball is dropped. Its first bounce is 400 feet high. It's second bounce is 320 feet high. Its third bounce is 256 feet high. Find the height of its twenty-eighth bounce to the nearest hundredth (2 decimal places).

0.97 feet

0.967 feet

Geometric Mean and Series

100

Find two geometric means between 5 and 135.

15 and 45

200

Find the sum of :

8,16,32... For the first 9 terms.

4088

300

Find the sum of the geometric series in which 

a₁ = 2000, a_n = 125, r = 1/2.

3875

400

What is the sum of the first eleven terms of a geometric sequence with r = -4 and first term 1?

838,861

500

Find the sum of the following sequence: 

3, 12, 48, ... , 196608.

262,143

Harmonic and Fibonacci

100

Given the fibonacci sequence 0, 1, 1, 2, 3, 5, 8,...

what is the 16th term?

610

200

Given the harmonic sequence 1/4, 1/7, 1/10, 1/13,...

what is a₁₅?

1/46

300

Find the 10th term of the fibonacci sequence 

-10, 3, -7, -4...

-108

400

What is the 7th term of the harmonic sequence 

1/2, 2/5, 1/3, 2/7, 1/4, ...?

1/5

500

Insert three harmonic means between 1/5 and 1/17.

1/8, 1/11, 1/14