Explicit Formulas
1. Arithmetic, Geometric, or Neither?
2. Find the explicit formula for:
4, 7, 10, 13, ...
1. Arithmetic
2. an= 3n + 1
1. Arithmetic, Geometric, or Neither?
2. Find the recursive formula for:
5, 8, 11, 14, ...
1. Arithmetic
2. a1 = 5
an = (an-1) + 3
Find the next three terms and the 18th term of the explicit sequence.
an = 3n - 5
-2, 1, 4, ..., 49
Does the following sequence have a limit?
If so, what is it? How do you know?
2, 4, 6, 8, 10, ...
No limit. The numbers keep getting bigger and bigger.
A tree’s height (in feet) is modeled by:
an = 12*(0.9)n , where n is in years.
7.09 ft
1. Arithmetic, Geometric, or Neither?
2. Find the explicit formula for:
3, -6, 12, -24, ...
1. Geometric
2. an = 3*(-2)n-1
1. Arithmetic, Geometric, or Neither?
2. Find the recursive formula for:
4, 12, 36, 108, ...
1. Geometric
2. a1 = 4
an = 3*(an-1)
Find the next 3 terms and the 9th term of the sequence.
4, 9, 14, 19, ...
24, 29, 34, ... , 44
Find the value of X in the sequence, when
a)Arithmetic
b) Geometric
6, X, 24
a) X = 15
b) X = +- 12
A formula for an investment account is modeled by:
an = 3000*(1+(0.05/12))n , where n is in months.
Find the value after 2 years.
$3314.82
1. Arithmetic, Geometric, or Neither?
2. Find the explicit formula for:
1, 1/2, 0, -1/2, ...
1. Arithmetic
2. an = (-1/2)n + 3/2
1. Arithmetic, Geometric, or Neither?
2. Find the recursive formula for:
67, 61, 55, 49, ...
1. Arithmetic
2. a1 = 67
an = (an-1) - 6
Find the first 4 terms of the sequence represented by the recursive formula:
a1 = 6
an = an-1 - 3
6, 3, 0, -3
Does the following sequence have a limit?
If so, what is it? How do you know?
1/2, 1/4, 1/8, 1/16, ...
Yes. Limit at 0 since the numbers are getting smaller and smaller.
A population of fish starts with 2000 fish and grows by 8% each year.
Find a formula for the fish population after n years.
an = 2000*(1.08)n
1. Arithmetic, Geometric, or Neither?
2. Find the explicit formula for:
64, 16, 4, 1, ...
1. Geometric
2. an = 64*(1/4)n-1
1. Arithmetic, Geometric, or Neither?
2. Find the recursive formula for:
81, 27, 9, 3, ...
1. Geometric
2. a1 = 81
an = (1/3)*(an-1)
Find the first 4 terms of the sequence represented by the recursive formula:
a1 = 2
an = 4*(an-1)
2, 8, 32, 128
Find the value of X in the sequence, when
a)Arithmetic
b) Geometric
10, X, 40
a) X = 25
b) X = +- 20
Franklin invests $1500 into a saving accounts that makes 6% interest and is compounded monthly.
Write an explicit formula for the value after n months.
an = 1500*(1+.06/12)n
or
an = 1500*(1.005)n
1. Arithmetic, Geometric, or Neither?
2. Find the explicit formula for:
2/3, 3/5, 4/7, 5/9, ...
1. Neither
2. an = (n+1) / (2n+1)
1. Arithmetic, Geometric, or Neither?
2. Find the recursive formula for:
(Hint: Think about the position of the number)
2, 4, 7, 11, 16, ...
1. Neither
2. a1 = 2
an = (an-1) + n
Find the next 3 terms and the 9th term of the sequence.
5, 7, 11, 19, ...
35, 67, 131, ... , 515
Does the following sequence have a limit?
If so, what is it? How do you know?
-5, 2, -1, 1, -0.5, 0.25
Yes. Limit at 0. Graph approaches 0. Values are getting smaller and smaller on both sides of axis.
Jimmy Bob invests $5000 into an account that makes 7% interest, compounded monthly.
a) Write an explicit formula for the value after n months.
b) Find the value after 4 years.
b) $6610.26