Pre-Calculus
Name________________
Assignment: K10
11.1 – 11.4, 11.6 Test Review
Find the first five terms of the sequence.
1.
𝑎𝑛 = 𝑛(2𝑛 − 1)
2.
𝑎𝑛 =
𝑎𝑛−1
, 𝑎1
2
= −8
4. 𝑎𝑛 = 𝑛𝑛
3. 𝑎𝑛 = −𝑎𝑛−1 + 2; 𝑎1 = 3
Find the sum.
4
5.
∑𝑘
5
2
6.
𝑘=1
∑(2𝑘 − 3)
𝑘=0
50
7.
Write the sum without sigma notation.
∑(2𝑛 − 1)
𝑛=0
Write the sum using sigma notation.
8.
2 + 4 + 6 + ⋯ + 20
9.
1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + ⋯ + 39 ∙ 40
Determine whether the sequence is arithmetic or geometric, then find the nth term of the sequence.
10.
3, 6, 9, 12, …
12.
The 12th term of an arithmetic sequence is 32 and the fifth term is 18. Find the 20th term.
11.
27, -9, 3, -1, …
13. Which term of the arithmetic sequence 1, 5, 9, … is 401?
3
2
14. The common ratio in a geometric sequence is , and the fifth term is 1. Find the 2nd term.
15. Find the partial sum 𝑆𝑛 of the arithmetic sequence with the given conditions: a = 3, d = 2, n = 12.
16. Find the sum of the arithmetic sequence: 0.7 + 2.7 + 4.7 + ⋯ + 56.7
20
17. Find the sum of the arithmetic sequence:
∑(1 − 2𝑛)
𝑘=0
18. The first term of an arithmetic sequence is 1 and the fourth term is 16. How many terms of this sequence
must be added to get 2356?
2
1
19. Find the partial sum 𝑆𝑛 of the geometric sequence with the given conditions: a = 3, r = 3, n = 4.
1
1
1
1
20. Find the sum of the geometric sequence: 1 − 2 + 4 − 8 + ⋯ − 512
5
21. Find the sum of the geometric sequence:
3 𝑘
∑ 7( )
2
𝑘=0
3
3
3
22. Find the sum of the infinite geometric series: 3 − 2 + 4 − 8 + ⋯
̅̅̅̅ as a fraction. YOU MUST SHOW WORK FOR THIS!!!!
23. Express 0.253
24. Find the amount of an annuity that consists of 24 monthly payments of $500 each into an account that
pays 8% interest per year, compounded monthly.
25. How much money should be invested every quarter at 10% per year, compounded quarterly, in order to
have $5000 in 2 years?
26. A couple can afford to make a monthly mortgage payment of $650. If the mortgage rate is 9% and the
couple intends to secure a 30-year mortgage, how much can they borrow?
27. What is the monthly payment on a 30-year mortgage of $80,000 at 9% interest?
a) What is the monthly payment on this same mortgage if it is to be repaid over a 15-year period?
b) What is the total amount paid on this loan over a 15-year period?
28. Jane agrees to buy a car for a down payment of $2000 and payments of $220 per month for 3 years. If
the interest rate is 8% per year, compounded monthly, what is the actual purchase price of her car?
Expand the expression (you can use EITHER Pascal’s Triangle or the Binomial Theorem).
29. (1 − 𝑥 2 )6
30. (2𝑥 + 𝑦)4
31. (2𝑥 + 𝑦 2 )5
32. (3𝑥 − 2𝑦)4
33.
Find the 20th term of the expansion (𝑎 + 𝑏)20 .
34.
Find the 26th term of the expansion (𝑥 − 𝑦)30 .
35.
Find the first three terms in the expansion of (𝑥 + 2𝑦) .
1
6
36.
Find the last three terms in the expansion of (2𝑥 3 − 𝑦 2 )5 .
37.
6
Find the term containing a in the expansion of (𝑎 + 3𝑏)10 .
38.
Find the term containing y 6 in the expansion of (2𝑥 2 − 𝑦 2 )5 .
Answers:
1. 1, 6, 15, 28, 45
2. -8, -4, -2, -1, -1/2
3. 3, -1, 3, -1, 3
10
7. -1 + 1 + 3 + 5 + ...+ 97 + 99
8. ∑ 2𝑛
9. ∑ 𝑛(𝑛 + 1)
𝑛=1
1 𝑛−1
3
12. a20 = 48
16. S29 = 832.3
18. n = 31 terms
22. 2
23.
251
990
24. Af = $12,971.67
27a) R = $811.41; 27b) $146,053.80
30. 16𝑥 4 + 32𝑥 3 𝑦 + 24𝑥 2 𝑦 2 + 8𝑥𝑦 3 + 𝑦 4
6. 12
10. Arithmetic, an = 3n
13. n = 101st term
19. 𝑆4 =
25. R = $572.34
28. $7,016.46
80
81
14. 𝑎2 =
20. 𝑆10 =
8
27
341
512
26. AP = $80,783.21
15. S12 = 168
21. 𝑆6 =
4655
32
27. R = $643.70;
29. 1 − 6𝑥 2 + 15𝑥 4 − 20𝑥 6 + 15𝑥 8 − 6𝑥 10 + 𝑥 12
31. 32𝑥 5 + 80𝑥 4 𝑦 2 + 80𝑥 3 𝑦 4 + 40𝑥 2 𝑦 6 + 10𝑥𝑦 8 + 𝑦10
32. 81𝑥 4 − 216𝑥 3 𝑦 + 216𝑥 2 𝑦 2 − 96𝑥𝑦 3 + 16𝑦 4
36. −40𝑥 6 𝑦 6 + 10𝑥 3 𝑦 8 − 𝑦10
5. 30
𝑛=1
11. Geometric, 𝑎𝑛 = 27 (− )
17. S21 = -399
4. 1, 4, 27, 256, 3125
39
37. 17010𝑎6 𝑏4
33. 20𝑎𝑏19
38. −40𝑥 4 𝑦 6
34.−142506𝑥 5 𝑦 25
35.
1
𝑥6
+
12𝑦
𝑥5
+
60𝑦 2
𝑥4