Sequences and Series Review

Basic Sequences

100

What does a₁ mean?

The first term

200

Find the first three terms of the sequence.

a_n= -1 + 6(n - 1)

-1, 5, 11

300

Find the next three terms of the sequence

25, 34, 43, 52,...

61, 70, 79

400

Find a₁₈ of the following sequence.

a_n = -3 - 8(n - 1)

-139

500

What is a₁₂ of this sequence?

5, 12, 19, 26,...

82

Arithmetic Sequences

100

What does d stand for?

The common difference.

200

Find d of the following sequence.

870, 750, 630, 510

d = -120

300

Find the explicit formula for the following sequence.

14, 11, 8, ...

a_n= 14 - 3(n - 1)

400

Find the 21st, 22nd, and 23rd term of the following sequence.

-10, -14, -18, -22

-90, -94, -98

500

Find the explicit formula of the following sequence.

-4, 1, 6, 11, ...

a_n = -4 + 5(n - 1)

Geometric Sequences

100

How do we find r?

a₂ ÷ a₁

200

Find r of the following series 

2, 14, 98, 686

r = 7

300

Find r of the following series 

8, 16, 32, 64,...

r = 2

400

Write the formula for the following geometric sequence.

375, 75, 15, 3, ...

Hint: a₁(r)^n-1

a_n= 375(1/5)^n-1

500

Write the explicit formula for the following geometric sequence.

7, -7, 7, -7, ...

Hint: a₁(r)^n-1

a_n= 7(-1)^n-1