Arithmetic and geometric

By Mai Nguyen, Marko Ilic, Liam Fortier, Ilija Mirkovic

7.1 Arithmetic Sequence Recap

• General formula: tn = a + d(n-1)
• a- first term; d - common difference; n -term number
• Recursive formula: t1 = a, tn = tn-1 + d

7.2 Geometric Sequence Recap

• General formula: tn - ar^n-1
• a - first term; r -common ratio; n - term number
• Recursive formula: t1 = a, tn= r(tn-1), n >1

1. The fifth term of an arithmetic sequence is 7 and the sixth term is 11. Find the seventh term.

Answer: 15

2. Determine which of the following sequences are geometric. For those sequences which are
geometric, find the common ratio.
a) 3, 15, 45, 135....
b) 3, 6, 12, 24.....
c) 120, 60, 30, 15.....
d) 400, 200, 0, -200, -400....

Answer:
a) geometric, common ratio = 3
b) geometric, common ratio = 2
c)geometric,common ratio= 1/2
d) not geometric

3. An interior designer is creating a wall fixture that will have 5 leaves on the first row, 15 leaves on
the second row, and 25 leaves on the third row. How many leaves will be on the 8th row?

Answer: 75 leaves

4. In an arithmetic sequence, t4 = 32 and t8 = 48. Find tn and t1, t2 & t3

Answer:
tn = 4n + 16
t1 = 20
t2 = 24
t3 = 28

5. In an arithmetic sequence,
t3 = 103 and t5 = 111. Find tn and t1, t2 & t12.

Answer:
tn = 4n + 91
t1 = 95
t2 = 99
t12 = 139

6. What is the 8th term of the geometric sequence:
2, 4, 8, 16, 32....

Answer: 256

7. Billy invests $1000 in an account that will earn 11 percent per annum; compounded annually,

create a geometric formula to represent how much his investment will be worth after each year.

Answer: 128

8. How many terms are there in the following sequence?
3, 6, 12, ..., 384

Answer: n = 16

9. How many terms are there in the following sequence?

16, 32, 64, …., 4096

Answer: n = 9

10. How many terms are there in the following sequence?
-111, -118, -125, -132,.., -251

Answer: n = 21

11. Explain how to determine whether a sequence is arithmetic.

Explain how to determine whether a sequence is geometric.

Answer: If the common difference is equal between each consecutive pair of terms, then the sequence is

arithmetic. If the common ratio is equal between each consecutive pair of terms, then the sequence is geometric.

12. In an arithmetic sequence, t4 = 32 and t8 = 48. Find tn and t1, t2 & t3.

Answer:
tn = 4n + 16
t1 = 20
t2 = 24
t3 = 28

13. What type of polynomial would be equivalent to an arithmetic sequence? What type of function would be equivalent to a geometric sequence?

Answer:
A linear equation. Because a linear equation has a common difference between consecutive integers.
An exponential equation. Because an exponential equation has a common ratio between consecutive integers.

14. In an arithmetic sequence, t3 = 103 and t5 = 111.
Find tn and t1, t2 & t12.

Answer:
tn = 4n + 91
t1 = 95
t2 = 99
t12 = 139

15. What is the 11th term of the arithmetic sequence:
11, 14, 17, 20, 23....

Answer: 41

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