Let's solve each sequence step by step and determine the next number in each pattern.
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Sequence A: 1, 3, 5, 7, ?
- This is an arithmetic sequence where each term increases by 2.
- The difference between consecutive terms is:
- \(3 - 1 = 2\)
- \(5 - 3 = 2\)
- \(7 - 5 = 2\)
- The next term will be:
\[
7 + 2 = 9
\]
-
Answer for A: \(11\)
---
Sequence B: 1, 4, 3, 6, 5, 8, ?
- This sequence alternates between two patterns:
1. Odd positions: \(1, 3, 5, \ldots\) (increasing by 2)
2. Even positions: \(4, 6, 8, \ldots\) (increasing by 2)
- The next term is in the 7th position (odd), so we continue the odd-position pattern:
- The last odd-position term is 5, and the next term is:
\[
5 + 2 = 7
\]
-
Answer for B: \(7\)
---
Sequence C: 1, 2, 4, 8, ?
- This is a geometric sequence where each term is multiplied by 2.
- The ratio between consecutive terms is:
- \(2 / 1 = 2\)
- \(4 / 2 = 2\)
- \(8 / 4 = 2\)
- The next term will be:
\[
8 \times 2 = 16
\]
-
Answer for C: \(16\)
---
Sequence D: 1, 3, 9, 27, 81, ?
- This is a geometric sequence where each term is multiplied by 3.
- The ratio between consecutive terms is:
- \(3 / 1 = 3\)
- \(9 / 3 = 3\)
- \(27 / 9 = 3\)
- \(81 / 27 = 3\)
- The next term will be:
\[
81 \times 3 = 243
\]
-
Answer for D: \(243\)
---
Sequence E: 90, 85, 75, 60, ?
- This sequence decreases by a pattern of subtracting increasing multiples of 5:
- \(90 - 5 = 85\)
- \(85 - 10 = 75\)
- \(75 - 15 = 60\)
- The next subtraction will be by \(20\):
\[
60 - 20 = 40
\]
-
Answer for E: \(40\)
---
Sequence F: 76, 65, 54, 43, 32, ?
- This is an arithmetic sequence where each term decreases by 11.
- The difference between consecutive terms is:
- \(65 - 76 = -11\)
- \(54 - 65 = -11\)
- \(43 - 54 = -11\)
- \(32 - 43 = -11\)
- The next term will be:
\[
32 - 11 = 21
\]
-
Answer for F: \(21\)
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Final Answers:
\[
\boxed{11, 7, 16, 243, 40, 21}
\]
Parent Tip: Review the logic above to help your child master the concept of sequence puzzles.
