Sequences And Series Review
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.