Number Sequences : Review
Multiple Choice
1. Given the sequence 2 , 8 , 14 , 20 , 26 , … What is the common difference ?
a) 2 b) 4 c) 6 d) 8
2. Find the 41st term in the sequence whose general term is .
a) 40 b) 157 c) 198 d) 221
3. What is the exponent on the x in simplified version of the expression (x-4 y2) -2 ?
a) -8 b) 8 c) -4 d) 4
4. Find the 11th term of the sequence tn = n(n - 6).
a) 55 b) 65 c) 75 d) 85
5. Find the 8th term of the sequence tn = 1600 (0.5)n-1
a) 6.25 b) 8.5 c) 12.5 d) 15.25
6. What is the next term in the geometric sequence -2 , 6 , -18 ,
a) 54 b) -54 c) 9 d) -9
7. Find the one arithmetic mean between -6 and 14.
a) 1 b) -4 c) 4 d) -8
8. What is the first term in the arithmetic sequence __ , 9 , __ , 33 , 45
a) -3 b) -1 c) 3 d) 6
9. What is the exponent on the b in the simplified version of (a3 b4)2 (a b5)2?
a) 5 b) 8 c) 9 d) 18
10. What is the common ratio in the sequence 12, -18, 27, ….
a) b) c) - d) -
Numerical Response
Numerical Responses. An answer sheet for these questions is found on the bottom of this page. Place the numbers and decimals in the blanks beginning at the left. Then color in the bubbles underneath each blank. 1 mark each.
1. What is the number of the last term shown in the following arithmetic sequence?
-8 , 2 , 12 , 22 , 32 , 42 , 52, … , 162 .
2. Calculate the sum of the arithmetic sequence -7 , 1 , 9 , 17 , … 105 .
3. The initial price of a car was $24 000. It will depreciate at the rate of 20% per year. Calculate the price of the car after 7 years. Round the answer to the nearest dollar.
4. Calculate the common ratio of the sequence 48 , 38.4 , 30.72 , 24.576 ? Round to the nearest tenth.
3. The first term of an arithmetic sequence is 8. The sum of the first 4 terms is 98 and the sum of the first 5 terms is 150. what is the common difference?
Written Response
Written Responses. Place your answers in the space provided.
1. Complete the spreadsheet for this loan payment.
Opening Balance / Rate / Interest / Payment / Closing Balance9 000 / 5% / $2 100
5% / $1 120
5% / $1 250
5% / $2 360
2. Find the next three terms, the general term and the specified term for the following arithmetic sequence.
-12, -20, -28, … t n = t 51 =
3. The general term for an arithmetic sequence is t n = 3n - 18. Find the sum of the first 66 terms.
4. The 1st term of an arithmetic sequence is 12 and the 9th term is 68. Find the sum of the first 18 terms.
5. Find the next three terms, the constant ratio and the specified term for the following geometric sequences.
6, 18, 54, … r = t 18 =
6. Determine the seating capacity of an auditorium with 36 rows of seats, if there are 15 seats in the first row, 18 seats in the second row, 21 seats in the third row, and so on.
Answers:
Multiple Choice : 1) c , 2) b , 3) b , 4) a , 5) c , 6) a , 7) c , 8) a , 9) d , 10) d
Numerical Response : 1) 18 , 2) 735 , 3) 6291 , 4) 0.8 , 5) 11
Written Response : 1) $3601.25 , 2) -412 , 3) 5445 , 4) 1287 , 5) 13122 , 6) 2430