Sequences And Series Review

33

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

12

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

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

¼

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

-146

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

-86

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

-88

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

113

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

117

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

176

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

202

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

2809

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

290

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

5(2)∧n-1

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

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

765

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

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.

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.

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.

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

an= -3n+8