HW #85 Answers:
6. an = 11n + 2, n ≥ 1
1. -2, 2, 6, 10, 14; arithmetic
b. 442
2. -6, -25, -44, -63, -82; arithmetic
c. n = 27
3. an+1 = an + 7, a1 = 14
4. an+1 = an + 10, a1 = -101
7. a. f(n) = -15n + 86, n ≥ 1
5. a. f(n) = 12n - 46, n ≥ 1
b. -229
b. f(n) = -.1n + .3, n ≥ 1
c. n = 67
c. f(n) = 4n + x, n ≥ 1
d. f(n) = an + n - 1, n ≥ 1
Mixed Review:
1. 12 feet by 18 feet
2. 3x2 - 10x - 10
Aim #86: How do we use arithmetic sequences to solve problems?
Do Now: Find the 99th term of -1, 2, 5, ...
Sean has started an exercise program. The first day he worked out for 30
minutes. Each day for the next six days, he increased his time by 5 minutes.
a) Write a general expression for an .
b) Write a recursive definition for this sequence.
c) If he ended up working out for 20 days, how long would he be working out
on the 20th day?
d) How many days into his exercise program would he be if he worked out
for 75 minutes?
e) Do you think we should restrict the domain of this sequence, and if so
what would be a realistic domain restriction?
1 ≤ n ≤ 31
If a1 = 3 and a5 = 27 are part of an arithmetic sequence, find the three
missing terms.
If a1 = -2 and a5 = 12 are part of an arithmetic sequence, find the three
missing terms.
Two terms of an arithmetic sequence are a8 = 21 and a27 = 97.
Find a rule for the nth term.
Two terms of an arithmetic sequence are a 31 = 18 and a73 = 46.
Find the sixth term.
3+x, 9+3x, 13+4x are terms of an arithmetic sequence for some value of x.
a. Find the value of x.
b. Find the 10th term of the sequence.
If the 84th term of a sequence is 515 and the common difference
is 6, find the 9th term.
If the 53rd term of a sequence is -524 and the common
difference is -10, find the 4th term.
Sum It Up!
We can use arithmetic sequences to solve harder problems by
utilizing the explicit formula: an = a1 + d(n - 1)