Sequences
Find the number of terms in the sequence: 20,23,26,…,59,62
What is 15? (u62 = 20+(n−1)×3 n)
The first term of an arithmetic sequence is -2 and the fifth term is 54. Find the common difference.
What is d = 14? (u54 = −2+4d)
The first term of a geometric sequence is 4 and the third term is 9. Calculate the common ratio.
What is r =1.5?
A garden watering system costs $389.95. As time goes on, its value depreciates by 42.50 per year. What is the value of the system after 4 years?
What is $219.95?
Explanation: https://docs.google.com/document/d/1GBEBwosmL6A-53ePhfj8qQJqqZH5G-y2BnYVpyYpp4I/edit?usp=sharing
The missing term in the sequence 2, 4, __, 16, 32
8
Consider the following sequence: −9,1,11,…,171,181 Find the number of terms in the sequence.
What is n = 20? (un = 181, 181 = −9+(n−1)×10)
Find the number of terms in the sequence: 20,23,26,…,59,62
What is n = 15? (u62 = 20+(n−1)×3)
Complete the table: https://docs.google.com/document/d/1moPB4pk0ytsVahIxQRHhc1KPDuDi4RwHpm8izPJexfo/edit?usp=sharing
Common ratio: 5, 3
Sum: 93, 78
A man works at the grocery store, he stacks tuna cans in rows, where there are 92 cans in the first row, 89 in the second row, 86 in the third row and so on. Find the number of cans in the 12th row.
Find the 10th term of the arithmetic sequence 2, 5, 8, 11...
Consider the following sequence: 32,41,50,…,185,194 Find the number of terms in the sequence.
What is n = 19? (un = 149, un = 32+(n−1)×9)
An arithmetic sequence has: u1 = 40, u2 = 32, u3 = 24. Find the common difference.
Then, find the 8th term.
A) What is d = -8?
(32 - 40 = -8)
B) What is u8 = -16?
u8 = u1 + (8-1)d
= 40 +(8-1)(-8)
Determine if these 6 sequences are geometric, if it is, find a common ratio.
1. -1, 6, -36, 216 2. -1, 1, 4, 8
3. 4, 16, 36, 64 4. -3, -15, -75, -375
5. -2, -4, -8, -16 6. 1, -5, 25, -125
1. R = -6 2. Not geometric
3. Not geometric 4. R = 5 5. R = 2
6. R = -5
A new business decides to rank its 9 employees by how well they work and pay them amounts that are in arithmetic sequence with a constant difference of $500 a year. If the total amount paid to the employees is 250,000, what will the employees make per year?
What is a1 = $25,778
Explanation: https://docs.google.com/document/d/1HweVMbfg8-e5u4hJBKF2uLQtP95m7qPk1mUh4d30kVA/edit?usp=sharing
Find the 5th term of the geometric sequence 3, 9, 27, 81...
What is 729?
The fifth term, u5, of a geometric sequence is 125. The sixth term, u6, is 156.25.
A) Find the common ratio of the sequence.
B) Find u1, the first term of the sequence.
A) What is r = 1.25?
(r = u6/u5 = 156.25/125)
B) What is u1 = 51.2?
(u1 = u5r1-5 = 125(1.25)1-5)
A bouncy ball is dropped out of a second story classroom window, 5m off the ground. Every time the ball hits the ground it bounces 89% of its previous height. Find the height that the ball reaches after the 2nd bounce.
What is approximately 3.96?
(u2 = u1r2-1 = 5(0.89)2-1)
The production of an oil well every year is 20% less than the year before. Find the total number of barrels produced in the first eight years given the production in the first year was 28,450. Then find the maximum production of the well.
Answer and Explanation:
https://docs.google.com/document/d/17gWspJy6aw4gP3I2cDXNtlWgNrbsNYAAMM6t_JA1Jzk/edit?usp=sharing
A ball is dropped from a height of 10 meters. Each time it bounces but reaches 80% of the height from which it fell.
A) write the height of the ball after each bounce as a geometric sequence. B) Find the height of the ball after the 5th bounce.
A) hn = 8 x (0.8) n-1
h1 = 10 x 0.8 = 8m (first term: a = 8, common ratio: r =0.8)
B) Approximately 3.28 m
h5 = 8 x (0.8)^4 = 8 x 0.4096 = 3.2768
The sum of the first 10 terms of an arithmetic sequence where the first term is 4 and the common difference is 3
The third term u3 of an arithmetic sequence is 7. The common difference d, is 3.
A) Find the first term
B) Find the 60th term
A) What is 1?
u1 = u3 + (1-1)(3)
= 7 +(1-1)(3) = 1.
B) What is 178?
u60 = u3 + (60-1)(3)
= 7 + (60-1) (3) = 178.
A small town has 1000 residents. Every year, the population doubled due to migration and birth rates.
1. Write down an expression for the population after n years.
2. What will be the population after 5 years?
3. If the town's resources can support up to 64,000 residents, after how many years will the population exceed this number?
1. P = 1000 x 2n
2. 32,000 residents (1000 x 25 = 1000 x 32 = 32000)
3. After 7 years
(Pn = 64,000. 1000 x 2^6 > 64,000 → 2^n > 64,000/1000 = 64, 22 > 64 → n > 6, smallest integer is n = 7)
A theater has 12 rows. The first row has 10 seats. Each row has 1.5 times as many seats as the previous one
A) Write down the number of seats in each row as a geometric sequence and find the number of seats in the 12th row.
B) If every third row is removed starting from the 3rd row (rows 3,6,9,12) how many rows remain?
A) Approximately 865 seats
(a = 10, r=1.5 → a12 = 10 x (1.5)11 = 10 x 86.49756 = 864.98)
B) 12 - 4 = 8
3,6,9,12 rows removed → total of 4 rows
The sum of the first 5 terms of a geometric sequence where the first term is 2 and the common ratio is -1
What is 2?