Math Problem Statement

1/2 7/8 5/4 13/8 find the next number in the pattern

Solution

To find the next number in the sequence 12,78,54,138\frac{1}{2}, \frac{7}{8}, \frac{5}{4}, \frac{13}{8}, let’s analyze how each term relates to the previous one.

  1. Convert to decimal form (to identify any potential pattern more easily):

    • 12=0.5\frac{1}{2} = 0.5
    • 78=0.875\frac{7}{8} = 0.875
    • 54=1.25\frac{5}{4} = 1.25
    • 138=1.625\frac{13}{8} = 1.625
  2. Calculate the differences between consecutive terms:

    • 0.8750.5=0.3750.875 - 0.5 = 0.375
    • 1.250.875=0.3751.25 - 0.875 = 0.375
    • 1.6251.25=0.3751.625 - 1.25 = 0.375

Each term increases by 0.3750.375, suggesting an arithmetic sequence with a common difference of 0.3750.375.

  1. Find the next term by adding 0.3750.375 to 1.6251.625: 1.625+0.375=2.01.625 + 0.375 = 2.0

In fractional form, 2.02.0 is 21\frac{2}{1}.

Answer:

The next number in the pattern is 21\frac{2}{1} or simply 22.

Would you like further details or have any questions?

Related Questions:

  1. What is an arithmetic sequence, and how is it identified?
  2. How can you convert fractions to decimal form accurately?
  3. What other types of sequences exist besides arithmetic?
  4. How do you identify a geometric sequence?
  5. How can sequences be applied in real-world scenarios?

Tip:

When analyzing sequences, checking the differences between terms can often reveal the underlying pattern easily.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Fractions to Decimals Conversion

Formulas

Next term in an arithmetic sequence: a_n = a_{n-1} + d

Theorems

Arithmetic Sequence Theorem

Suitable Grade Level

Grades 6-8