Math Problem Statement

Test lI. ldentify the next term in the pattern.

  1. ABA, CDC, EFE, GHG, ___
  2. 12, 13, 15, 18, 22,__
  3. 7, 20, 47, 94, 167, ___
  4. 1,4, 2, 8, 6, 24, 22,____
  5. 11, 23, 48, 99, _____HH 6.6, 13, 27, 55, 111, ___
  6. 8, -24, 72, -216, 648, -1944,____
  7. R2BC, S3DE, T4FG, _____
  8. 34, 7, 37, 14, 40, 28, ___
  9. 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:

  1. 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
  2. 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
  3. 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
  4. 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
  5. 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. 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
  7. 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
  8. 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
  9. 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
  10. 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:

  1. How do arithmetic sequences differ from geometric sequences?
  2. What is the general formula for the nth term of an arithmetic sequence?
  3. How can you determine the common difference in a sequence?
  4. What strategies can you use to identify patterns in non-linear sequences?
  5. 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