Math Problem Statement

Find the Nth term of the following 1. 1,5,9 13,… 27th term 2. 20, 15, 10,… 66th term 3. 100, 92, 84, … 48th term 4. 7, 14, 21,… 89th term 5. 1, 1/2, 0,… 16th term

Solution

To find the NNth term of each sequence, we'll use the formula for the NNth term of an arithmetic sequence:

aN=a1+(N1)da_N = a_1 + (N-1) \cdot d

Where:

  • aNa_N is the NNth term,
  • a1a_1 is the first term,
  • dd is the common difference between the terms,
  • NN is the position of the term in the sequence.

Let's solve each one.

1. Sequence: 1, 5, 9, 13, …

  • First term a1=1a_1 = 1
  • Common difference d=51=4d = 5 - 1 = 4
  • To find the 27th term (N=27N = 27):

a27=1+(271)4=1+264=1+104=105a_{27} = 1 + (27 - 1) \cdot 4 = 1 + 26 \cdot 4 = 1 + 104 = 105

The 27th term is 105.

2. Sequence: 20, 15, 10

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences

Formulas

Nth term formula for arithmetic sequences

Theorems

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Suitable Grade Level

Grades 7-9