Arithmetic Sequence Formula

Arithmetic sequence formula is used to calculate the nth term of an arithmetic sequence. To recall, a sequence is an ordered list of numbers. The sum of the terms of a sequence is called a series. An arithmetic sequence or arithmetic progression is a sequence in which each term is created or obtained by adding or subtracting a common number to its preceding term or value. In other words, the difference between the adjacent terms in the arithmetic sequence is the same.

Formulas of Arithmetic Sequence

For the formulas of an arithmetic sequence, it is important to know the 1st term of the sequence, the number of terms and the common difference. Now,

Arithmetic Sequence Formulas
nth Term Formula an = a1 + (n – 1)d
Sum of First n Terms Sn = n/2 (first term + last term)

Where,

  • an = nth term that has to be found
  • a1 = 1st term in the series n
  • n = the number of terms
  • d = the common difference
  • Sn = the sum of n terms

A solved problem on the arithmetic sequence is given below.

Solved Example Using Arithmetic Sequence Formula

Question 1: Find the 16th term in arithmetic sequence 0, 2, 4, 6, 8, 10, 12, 14…..?
Solution:

The arithmetic sequence is given as,

an = a1 + (n – 1)d

From the given problem,

a1 = 0 ;

n = 16 ;

d = 2

a16 = 0 + (16 – 1)2

a16 = 0 + (15 × 2)

a16 = 0 + 30

a16 = 30

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