HW #84 Answers:
1. 11, 17, 23, 29, 35
2. 25, 12.5, 6.25, 3.125, 1.5625
3. 1, 6, -4, 16, -24
4. 6, 9, 13, 18, 24
5. 2, 10, 50, 250, 1250
12. a. an+1 = an - 8, a1 = 9, n ≥ 1
b. an = 17 - 8n, n ≥ 1
c. -287
6. an+1 = an + 1, a1 = 8 ,n ≥ 1
7. an+1 = 10an , a1 = 4, n ≥ 1
8. an+1 = an - 3 , a1 = -1, n ≥ 1
9. an+1 = 12an , a1 = -1, n ≥ 1
10. an+1 = an + 3000 , a1 = 30000, n ≥ 1
11. an+1 = 3an , a1 = 10, n ≥ 1
Mixed Review:
1. 18 nickels and 15 dimes
13. an+1 = an2, a1 = 2, n ≥ 1
2. x = -94/7
Aim #85: What is an arithmetic sequence?
Do Now: Write the recursive formula and find the next term for:
a. 2, 5, 8, 11, ...
b. 8, 19, 30, 41, ...
A sequence is called arithmetic if there is a real number, d, such that
each term in the sequence is the sum of the previous term and d.
Arithmetic sequences are often called "linear sequences."
Write the recursive and explicit formula for the following sequences:
b. -2, -3, -4, -5, ...
a. 4, 6, 8, 10, ...
Recursive:
Recursive:
Explicit:
Explicit:
To find a general formula for an arithmetic sequence:
an = a1 + d(n - 1)
where an is the value of the nth term, a1 is the first term, and d is
the common difference. We then simplify to get the formula in the
easiest form to work with.
The recursive formula is
an+1 = an + d
1) Determine if each of the following formulas is recursive or
explicit and then write out the first 5 terms. Write the other
formula as well.
a. an = 3n - 2, n ≥ 1
b. f(n+1) = f(n) - 8, f(1) = 15
c. an = an-1 + 3, a1 = -4
d. f(n) = -2n + 5, n ≥ 2
2) Given the following sequences, determine if they are arithmetic
or not. If they are, find the common difference and determine a
formula to find the nth term.
a. 24, 20, 16, 12,...
b. 3, 5, 9, 15, 23,...
c. -2, -5, -8, -11, ...
d. w+3, 3w+8, 5w+13, ...
3)If a1 = 4 and d = 3, find the rule for a n .
b) What is the 11th term?
c) If the nth term of the sequence is 307, find the value of n.
4)Given the sequence -1, -7, -13, -19, ... find the rule for a n .
b) What is the 30th term?
c) If the nth term of the sequence is -577, find the value of n.
5)Given the sequence f(n) = f(n-1) + 11, f(1) = -9, find the explicit
rule for f(n).
b) What is the 88th term?
c) If the nth term of the sequence is 3434, find the value of n.
Sum It Up!
An arithmetic sequence has a common difference.
Recursive: an+1 = an + d
Explicit: an = a1 + d(n - 1) , n≥1