Arithmetic Sequences (HW#18)
KEY SKILLS
For questions 1 – 4 determine if the sequence shown is arithmetic or not. If it is, state the common difference.
1. 10, 8, 6, 4, 2, …
1 2 4 8 16
,
3
2. 3, 3, 3, 3,
…
5
3
3. 3, 2, 2, 2, 1, …
4. 12, 22, 32, 42, 52, …
5. Find the 13th term of the arithmetic sequence: 4.2, 6.6, …
6. List the first 5 terms of the arithmetic sequence given that its 8th term is 26 and its 12th term is 42.
7. List the first 5 terms of the arithmetic sequence given that its 6th term is –38 and its 11th term is –73.
8. Find the 50th partial sum of the sequence –6, –2, 2, 6, …
9. Find the indicated sum: ∑20
𝑛=1(2𝑛 − 5)
10. A brick patio plan has a trapezoidal shape where the first row has 44 bricks and the 18th row has 61 bricks. How
many bricks will need to be purchased to create the brick patio as outlined on the plan?
11. A small auditorium plans to have 15 rows of seats with each row having two more seats than the row before it. If
the first row has 25 seats, how many seats will there be in total?
REVIEW ITEMS
1. Expand the logarithm until it is the sum/difference of logs with no exponents
log
𝑥2𝑦
𝑧4
=?
2. Condense the logarithm until it is a single logarithmic expression
1
3
2 ln x – 3 ln y – ln z = ?
Evaluate each expression using properties of logarithms
3. log6 27 + log6 8
4
5. log7 √7
4. log9 1
1
6. log3 81
7. 4 ln e3
Solve each equation below. Be sure to have an exact answer AND a decimal approximation
8. ln(3x – 2) = 2
9. 22x = 200
Using the compound interest formulas: A
𝑟
= P(1 + )nt and A = Pert
𝑛
10. 5e3x – 4 = 50
answer questions 11 – 12
11. If $15,000 is deposited into an account that has an interest rate of 8% and compounds continuously, how much
money will be in that account after 35 years?
12. Suppose your grandparents started an account 40 years ago with an initial investment of $10,000. If the account
compounds quarterly and now has $237.699.07 in it, what was the interest rate?
13. The sales S(in thousands) of a new technology unit after it has been on the market for t years is given by S
= 100(1 – ekt). If 40,000 of the unit were sold in the first year, how many will sell after 5 years?