Lists that multiply each step

Mathematics · Algebra · ages 15-16

Name ______________________ Date ____________

The sequence starts 5, 15, 45. What is the next term?
Answer: ______________
The sequence starts 3, 6, 12, 24. What is the common ratio?
- 3
- 2
- 4
- 6
The sequence starts 3, 6, 12, 24. 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 100, 50, 25. What is the 5th term?
Answer: ______________
The sequence starts 100, 50, 25. What is the 5th term?
Answer: ______________
First term 4, common ratio 3. What is the 4th term?
- 108
- 36
- 48
- 324
Priya says a common ratio of 0.5 makes the terms shrink toward zero. Is Priya right?
Circle one: True False
First term 5, common ratio 2. Which term equals 320?
- 7
- 5
- 6
First term 3, common ratio 4. What is the 4th term?
Answer: ______________

Answer key

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

135 · The ratio is 15 over 5 = 3, so 45 times 3 = 135.
2 · 6 divided by 3 is 2, and each later division matches. The 3 option is the difference, not the ratio.
2 · Divide neighbours: 6 divided by 3 = 2.
True · First term 2 and ratio 3 give exactly that rule, and n = 1 returns 2.
6.25 · Ratio 0.5, so term 5 = 100 times 0.5 to the power 4 = 100 times 0.0625 = 6.25.
6.25 · Ratio 0.5, so the terms run 100, 50, 25, 12.5, 6.25.
108 · Term 4 = 4 times 3 cubed = 4 times 27 = 108. The 36 option is term 3.
True · Multiplying by 0.5 repeatedly halves every term, so values approach zero but stay positive.
7 · 5 times 2^(n-1) = 320 gives 2^(n-1) = 64, so n - 1 = 6 and n = 7.
192 · Term 4 = 3 times 4 cubed = 3 times 64 = 192.