Math Problem Statement

0, 5, 10, 8, 13, 26, 24, 29, ...., 56, 61 (A) 27 (B) 48 (C) 56 (D) 58 (E) 60

Solution

Let's break down the sequence step by step:

Given the sequence:
0, 5, 10, 8, 13, 26, 24, 29, ..., 56, 61

We can observe the changes between consecutive numbers:

  1. From 0 to 5: +5
  2. From 5 to 10: +5
  3. From 10 to 8: -2
  4. From 8 to 13: +5
  5. From 13 to 26: +13
  6. From 26 to 24: -2
  7. From 24 to 29: +5

It appears that the pattern alternates between adding 5, then adding a larger number (either 13 or another larger number), and sometimes subtracting 2.

Let’s predict the next term based on this alternating pattern. From 29, the next step seems to follow the addition pattern (since we previously added 5 from 24 to 29).

The next number could logically be 48, since:

  • The next addition step should follow the same logic as from 26 to 24, which was -2. The alternating pattern would now lead us to add 19, as it makes sense given the larger steps we see earlier in the sequence (like +13 and the expected growth).

Thus, the next term is 48.

Answer: (B) 48


Would you like further clarification or a deeper breakdown? Here are 5 related questions for you to consider:

  1. What type of sequence is this (arithmetic, geometric, or another)?
  2. How do alternating patterns influence sequences like this?
  3. Can you predict the next few terms after 48 based on this logic?
  4. How does the alternating addition/subtraction pattern evolve in other similar sequences?
  5. What happens if the alternating pattern is disrupted, for example by replacing addition with subtraction?

Tip: When analyzing sequences, always check if there’s a consistent pattern in the differences between terms. Alternating sequences often involve regular additions and subtractions, which can reveal a deeper structure.

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Math Problem Analysis

Mathematical Concepts

Number Sequences
Pattern Recognition
Arithmetic Progressions

Formulas

Difference between consecutive terms

Theorems

Arithmetic sequence properties

Suitable Grade Level

Grades 6-8