Sequences Review

TERMS/CONCEPTS

100

A sequence which has a specific order Known as____

PATTERN

200

It is denoted by d

Common Difference

300

It is a sequence which has a common difference

Arithmetic Sequence

400

It is obtained by dividing the succeeding term to the preceding term.

common ratio

500

It is the sum of all the terms in an arithmetic sequence.

Arithmetic Series/sequence

Sequence Types

100

Is the sequence arithmetic, geometric, or neither?

6, 3, 0, -3, -6, ...

arithmetic 

200

is the sequence arithmetic, geometric, or neither?

9, 36, 144, 576, 2304, ...

geometric

300

What type of sequence is: 

1, 1, 2, 3, 5, 8, 13, 21, 54,...?

Fibonacci Sequence

400

Is the sequence harmonic or not?

1/5, 1/9, 1/13, 1/17,....?

Harmonic

500

Is the sequence arithmetic, geometric, or neither?

a₁ = 8,  a_{2 = 11,  a3 = 16} 

neither

General Formula

100

Formula in finding d in an arithmetic sequence.

a₂ - a₁

200

General formula in finding the sequence in an arithmetic sequence.

 a_n = a₁ + (n-1)d

300

Formula in finding S_n in an arithmetic sequence whose a₁ and a_n are given.

Sn = n/2( a₁ + a_n)

400

A geometric sequence starts

4, 16, ...

Write an explicit definition for it.

 4ⁿ

500

Write the general formula in the sequence: 

2, 4, 8, 16,..

 2ⁿ

Missing Term

100

Using the sequence: 3, 7, 11, ...,what is the 5th term?

19

200

Given the sequence:  6, 12, 24..., what is the common ratio?

 r = 2

300

How many terms are there in a sequence if the last term is (-20), a₁ = 5 and the common difference is (-5)?

n = 6

400

Find the second geometric mean in a sequence:

4,___, ___, 108?

r = 3, therefore the second geometric mean is 36.

500

What is the sum of the first 12 even numbers from 5 t0 29?

S_n = 204