Sequences And Series Review

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Find sum of first 30 odd natural numbers ( 1+3+...+59)

900

Arithmetic Sequence

ADD a constant amount, d, to get the next term. Find d by SUBTRACTING a term by the previous term.

a₁ + d (n - 1)

Arithmetic sequence

Convergent Tests

Arithmetic sequences do not converge. Geometric converges only for |r| < 1. Other sequences converge according to function convergence rules.

Common Difference d

Determines Arithmetic sequence

Common Ratio r

Determines Geometric sequence

96

Find the number of terms: -3, -7, -11, ...-383

35

Find the number of terms: 2, 4, 6, 8, ...., 70

16,400

Find the sum of the first 8 terms: 5, 15, 45, 135,...

a₁ × rⁿ⁻¹

Geometric sequence

Geometric Sequence

MULTIPLY a constant amount, r, to get the next term. Find r by DIVIDING a term by the previous term.

-2, 3, 8, 13, ... Find term 24

113

9, 12, 15, 18, ... Find term 37

117

Initial population of 600 penguins triples in size each year for six years. Find size of population after six years

145,800

0, 8, 16, 24, ... Find term 23

176

Find sum to infinity of the geometric series; 3- ³/₂+³/₄-...

2

4, 10, 16, 22, ... Find term 34

202

18, 118, 218, 318, ... Find term 23

2218

Find sum to infinity of the geometric series; ¹/₅ - ¹/₅⁴+¹/₅⁷-...

25/126

Find sum to infinity of the geometric series; 5 + 1+¹/5+...

25/4

9, 109, 209, 309, ... Find term 29

2809

-20, -10, 0, 10, ... Find term 32

290

-7, 93, 193, 293, ... Find term 40

3893

The first three terms of a geometric series are 5,10,10. Find Tn (nth term)

5(2)∧n-1

Find sum to infinity of the geometric series; 1+(²/₅)+(²/₅)²+...

5/3

Find sum of the first eight terms of the geometric series; ½+¼+¹/₈ +...

510/512

-12, 8, 28, 48, ... Find term 30

568

20, 220, 420, 620, ... Find term 32

6220

Find sum of the first eight terms of the geometric series; 3+6+12+...

765

Find the explicit form: 5, 2, -1, -4, -7, ....

an= -3n+8

33

find the number of terms: 12,18,24,30....204

12

find the number of terms: 5, 9, 13, 17, ... 49

The Geometric Sequence Infinite Sum

where a is the first term and |r| < 1

The first two terms of a geometric series are 216+54. Find common ration

¼

The sum to infinity of a geometric series is twice the first term. Find then common ratio

½

-30, -230, -430, -630, ... Find term 26

-5030

-32, -34, -36, -38, ... Find term 28

-86

28, 24, 20, 16, ... Find term 30

-88

-6, -13, -20, -27, ... Find term 21

-146

-27, -31, -35, -39, ... Find term 35

-163

How can you find the eleventh term of a sequence given the 4th term and a common difference d?

Use the explicit formula to determine the first term, then use again to determine the eleventh.

Explicit Formula for Arithmetic Sequence

Relates any term in a sequence to only the first term and the common difference.

Explicit Formula for Geometric Sequence

Relates any term in a sequence to only the first term and the common ratio.

Recursive Formula for Arithmetic Sequence

Relates any term in a sequence to only the prior term and the common difference.

Recursive Formula for Geometric Sequence

Relates any term in a sequence to only the prior term and the common ratio.

Arithmetic

State if it is arithmetic, geometric, or neither.

Geometric

State if it is arithmetic, geometric, or neither.

Neither

State if it is arithmetic, geometric, or neither.


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