Lists that multiply each step

Mathematics · Algebra · ages 15-16

Name ______________________ Date ____________

The sequence starts 6, 12, 24. What is the next term?
Answer: ______________
The sequence starts 7, 21, 63, 189. What is the common ratio?
- 14
- 3
- 7
- 1/3
The sequence starts 2, 8, 32, 128. What is the common ratio?
Answer: ______________
The nth term of 2, 6, 18, ... is 2 times 3^(n-1).
Circle one: True False
The sequence starts 64, 16, 4. What is the 5th term?
Answer: ______________
The sequence starts 80, 40, 20. What is the 5th term?
Answer: ______________
First term 3, common ratio 4. What is the 4th term?
- 48
- 768
- 192
- 64
Kai says 90, 30, 10, ... has a ratio between 0 and 1, so its terms shrink toward zero. Is Kai right?
Circle one: True False
First term 5, common ratio 2. Which term equals 320?
- 7
- 5
- 6
First term 5, common ratio 2. What is the 6th term?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

48 · The ratio is 12 over 6 = 2, so 24 times 2 = 48.
3 · 21 divided by 7 is 3, and each later pair matches. 14 is the difference, not the ratio.
4 · Divide neighbours: 8 divided by 2 = 4, and 32 divided by 8 = 4.
True · First term 2 and ratio 3 give exactly that rule, and n = 1 returns 2.
0.25 · The ratio is 1/4, so the terms run 64, 16, 4, 1, 0.25.
5 · Ratio 0.5, so the terms run 80, 40, 20, 10, 5.
192 · Term 4 = 3 times 4^3 = 3 times 64 = 192. 48 is term 3 and 768 is term 5.
True · The ratio is 30 over 90 = 1/3, which sits between 0 and 1, so each term is a third of the last.
7 · 5 times 2^(n-1) = 320 gives 2^(n-1) = 64, so n - 1 = 6 and n = 7.
160 · Term 6 = 5 times 2^5 = 5 times 32 = 160.