General Sequences and Series
Arithmetic Sequences
Geometric Sequences
Arithmetic Series
Geometric Series
1

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.

1

Given that a1 = 7 and d=2, what is the 5th term

15

1

For the given sequence, find the common ratio and the 9th term:

1/2, 2, 8, ...


r = 4

a12 = 32,768

1

Find S(Note: NOT t9)

13, 15, 17, ...

S9 = 189

1

Find S7 for the following sequence:

-2, -12, -72, ...

S7 = -3110

1

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).

1

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


9, 12, 15, 18, ...

d = 3

a10 = 36

1

Given that a1 = -5 and an = -5(2)n-1, find a6.

a6 = -160

1

Evaluate the given series.

S10 = 365

1

Evaluate the given series:

S9 = 39,364

2

arithmetic series has a common _____

difference

2

Find three arithmetic means between -3 and 29. 

-3, __, __, __, 29

5, 13, 21

2

Find two geometric means between 6 and 162.

6, __, __, 162

18, 54

2

Evaluate the following arithmetic series:

t1 = 42, t14 = 146

1316

2

Find the S9 

1 , 0.5  , 0.25  ...

1/256

3

There are 130 students in grade 1, 210 students in grade 2, and 290 students in grade 3 in a primary school, and so on in an arithmetic sequence. What's the total amount of students in the school? (there are 6 grades in the school).

1980 students

3

Given the explicit formula below, find the first four terms and a15.

an = -11+(n-1)7

-11, -4, 3, 10

a15 = 87

3

Given the explicit formula below, find the first four terms and a10 (round to nearest thousandth).

an = (1200)(1/2)n-1

1200, 600, 300, 150

a10 = 2.344

3

Determine the number of terms in the arithmetic series:

-1 + 2 + 5 + ... + 68

n = 24

3

Find S12

4n-7

228