Math Problem Statement
Test lI. ldentify the next term in the pattern.
- ABA, CDC, EFE, GHG, ___
- 12, 13, 15, 18, 22,__
- 7, 20, 47, 94, 167, ___
- 1,4, 2, 8, 6, 24, 22,____
- 11, 23, 48, 99, _____HH 6.6, 13, 27, 55, 111, ___
- 8, -24, 72, -216, 648, -1944,____
- R2BC, S3DE, T4FG, _____
- 34, 7, 37, 14, 40, 28, ___
- 16384, 8192, 2048, 256, 16, ______
The image should be like to show the solution
Solution
To solve the patterns in the provided image, I'll analyze each sequence individually:
-
ABA, CDC, EFE, GHG, ___
The pattern follows an increasing alphabetical sequence for both the first and third letters, while the middle letter remains constant and progresses alphabetically.- A, C, E, G → The next letter in sequence is I.
- B, D, F, H → The next letter is J.
- The third letter is a repetition of the first. Answer: IJI
-
12, 13, 15, 18, 22, __
The pattern appears to be increasing by sequentially larger increments.- 12 → 13 (+1)
- 13 → 15 (+2)
- 15 → 18 (+3)
- 18 → 22 (+4)
- The next increment should be +5. Answer: 27
-
7, 20, 47, 94, 167, ___
The pattern seems to be adding sequentially larger odd numbers to each term.- 7 → 20 (+13)
- 20 → 47 (+27)
- 47 → 94 (+47)
- 94 → 167 (+73)
- The next increment is 73 + 28 (as it follows an increment of 14, 20, 26, 28 in increments). Answer: 270
-
1, 4, 2, 8, 6, 24, 22, ____
The sequence alternates between multiplication by 4 and subtraction of 2.- 1 → 4 (×4)
- 4 → 2 (−2)
- 2 → 8 (×4)
- 8 → 6 (−2)
- 6 → 24 (×4)
- 24 → 22 (−2)
- The next step should be multiplication by 4. Answer: 88
-
11, 23, 48, 99, ____
The pattern increases by successively larger numbers, which seem to follow a specific pattern.- 11 → 23 (+12)
- 23 → 48 (+25)
- 48 → 99 (+51)
- The increments double each time, so the next increase should be 102. Answer: 201
-
6, 13, 27, 55, 111, ____
The sequence follows a pattern of doubling and subtracting one.- 6 → 13 (×2 + 1)
- 13 → 27 (×2 + 1)
- 27 → 55 (×2 + 1)
- 55 → 111 (×2 + 1)
- The next step follows the same pattern. Answer: 223
-
8, -24, 72, -216, 648, -1944, ____
This is a geometric sequence where each term is multiplied by -3.- 8 × (-3) = -24
- -24 × (-3) = 72
- 72 × (-3) = -216
- -216 × (-3) = 648
- 648 × (-3) = -1944
- -1944 × (-3) = 5832 Answer: 5832
-
R2BC, S3DE, T4FG, ____
The pattern involves an increment in both the letter and the number.- R → S → T → U
- 2 → 3 → 4 → 5
- BC → DE → FG → HI Answer: U5HI
-
34, 7, 37, 14, 40, 28, ____
This sequence seems to alternate between adding 3 and subtracting 27.- 34 → 7 (−27)
- 7 → 37 (+30)
- 37 → 14 (−23)
- 14 → 40 (+26)
- 40 → 28 (−12)
- Next, it would add 3. Answer: 31
-
16384, 8192, 2048, 256, 16, ____
The sequence divides by 2, 4, 8, 16.- 16384 ÷ 2 = 8192
- 8192 ÷ 4 = 2048
- 2048 ÷ 8 = 256
- 256 ÷ 16 = 16
- 16 ÷ 32 = 0.5 Answer: 0.5
Would you like further details on any of these solutions?
Here are 5 questions related to this topic:
- How do arithmetic sequences differ from geometric sequences?
- What is the general formula for the nth term of an arithmetic sequence?
- How can you determine the common difference in a sequence?
- What strategies can you use to identify patterns in non-linear sequences?
- How do alternating sequences influence the pattern recognition process?
Tip: When analyzing number sequences, pay close attention to the differences between terms, as they often provide clues to the underlying pattern.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Number Patterns
Arithmetic Sequences
Geometric Sequences
Formulas
-
Theorems
-
Suitable Grade Level
Grades 7-9
Related Recommendation
Number Sequence and Pattern Puzzle Solved: Sequence and Logical Patterns for Grades 6-9
Solutions to Arithmetic Sequences and Matrix Representation Problems
Solutions to Sequence Problems: Finding Missing Numbers
Sequence and Progression Problems - Grade 6 to 9 Math
Find the Missing Numbers in Number Sequences - Problem and Solution