PRACTICE Advanced Trig Test on Chapter 11 Sections 1 – 7
Name: _________________________
𝑡𝑛 = 𝑡1 + (𝑛 − 1)𝑑
Sequences and Series
𝑡𝑛 = 𝑡1 ∙ (𝑟)(𝑛−1)
Some useful formulas are in the box for you.
Round/truncate all decimal values to three places.
𝑆𝑛 =
𝑛
𝑡1 + 𝑡𝑛
(𝑡1 + 𝑡𝑛 ) 𝑜𝑟 𝑛 (
)
2
2
𝑆𝑛 = 𝑡1 ∙
𝑆 = lim
𝑛→∞
1 − 𝑟𝑛
1−𝑟
𝑆𝑛 = 𝑡1 ∙
1
1−𝑟
Label the following as either a sequence or a series, arithmetic or geometric or neither.
Example
1.
2.
3.
4.
5.
6.
Sequence or Series
Arithmetic or Geometric or
Neither
2+4+6+8+...
2, 10, 50, 250, . . .
1, 1, 2, 3, 5, . . .
-1 + 2 – 5 + 9 - . . .
60 + 30 + 15 + 7.5 + . . .
𝑛
∑ 6 + 3(𝑛 − 1)
𝑘=1
7.
𝑛
∑ 4(1.2)(𝑛−1)
𝑘=1
For the following: Write out the first FOUR terms on the four dashes provided.
6. An Arithmetic series where the first term is 4 and the common difference is 1.2
_________ _________ _________ __________
7. A Geometric series where 𝑡1 = 20 and r = .82
___________ ______________ _____________ ______________
8. ∑𝑛𝑘=1 6 + 3(𝑛 − 1)
_________ _________ _________ __________
9. ∑𝑛𝑘=1 4(1.2)(𝑛−1)
__________ __________ __________ ___________
10. For the arithmetic sequence 16 + 21 + 26 + 31 + . . .
a. find the fifth term
b. find term 2000 and 2001
c. 3041 is a term in the sequence, which term is it?
11. For the geometric sequence where the first term is 23 and the common ratio is 0.4
a. find the 7th term
b. .0376832 is an approximation of a term in this sequence, which term is it?
c. This term converges, what does it converge to? (round/truncate to three decimal places)
12. The value 49.7664 exactly is the sixth term of a geometric sequence where the common ratio is 1.2,
find the first term.
13. Find the 100th term partial sum for the following:
a. an arithmetic sequence whose common difference is + 4 and whose first term is 13.
b. an geometric sequence whose common ratio is 1.5 and whose first term is 0.3.
14. An arithmetic sequence has a first term of 82 and a common difference is 6. Is the value 300 a term
in this sequence? Why or why not?
15. Assume that the number of inches a tree grows each year is a term in a geometric series. Suppose
that you plant a tree that grows 50 inches the first year and 42 inches the next year.
a. predict how much it will grow in the 6th year.
b. How tall will the tree be after 10 years?
c. Predict what might be the ultimate height of the tree?
16. Peter invests $420 into a savings account that yields an interest rate of 3.78% per year interest
compounded annually (once a year). How much will Peter have after 10 years?