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What is the 21st term of the arithmetic progression 5 9 13 by using formula?

Published in Arithmetic Progressions 2 mins read

The 21st term of the arithmetic progression 5, 9, 13 is 85. This can be confirmed using the arithmetic progression formula.

Understanding Arithmetic Progressions

An arithmetic progression (AP) is a sequence of numbers such that the difference between any two consecutive terms is constant. This constant difference is called the common difference.

  • First term (a): The first number in the sequence.
  • Common difference (d): The constant difference between consecutive terms.
  • nth term (an): The term at the nth position in the sequence.

Formula for the nth term of an AP

The formula to find the nth term of an arithmetic progression is:

an = a + (n - 1)d

Where:

  • an is the nth term
  • a is the first term
  • n is the term number
  • d is the common difference

Applying the Formula

In the given arithmetic progression 5, 9, 13:

  • a = 5 (the first term)
  • To find d (the common difference), subtract the first term from the second term: d = 9 - 5 = 4

We want to find the 21st term (a21), so n = 21.

Plugging these values into the formula:

a21 = 5 + (21 - 1) * 4
a21 = 5 + (20) * 4
a21 = 5 + 80
a21 = 85

Therefore, the 21st term of the arithmetic progression is indeed 85, as indicated by the reference.

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