Math Problem Statement

7, 20, 47, 94,

Solution

The sequence provided is: 7, 20, 47, 94, ...

To identify the pattern and find the next term, let's analyze the differences between consecutive terms:

  1. 207=1320 - 7 = 13
  2. 4720=2747 - 20 = 27
  3. 9447=4794 - 47 = 47

The differences between consecutive terms are: 13, 27, and 47.

Let's examine these differences further:

  • The difference between 13 and 27 is 2713=1427 - 13 = 14.
  • The difference between 27 and 47 is 4727=2047 - 27 = 20.

It seems the second differences are increasing by 6. This suggests the sequence follows a pattern where the difference between consecutive terms increases by an incrementally larger amount each time.

To find the next term:

  • The next difference would be 47+20+6=7347 + 20 + 6 = 73.
  • Adding this difference to the last term, 94+73=16794 + 73 = 167.

So, the next term in the sequence

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Math Problem Analysis

Mathematical Concepts

Sequences
Arithmetic Sequences
Patterns in Sequences

Formulas

n-th term of an arithmetic sequence: a_n = a_1 + (n-1) * d

Theorems

Arithmetic sequence theorem

Suitable Grade Level

Grades 7-9