Arithmetic Sequence Formula

Arithmetic sequence formula is used to calculate the nth term of an arithemetic sequence. To recall, a sequence is an ordered list of numbers. The sum of the terms of a sequence is called a series. Arithmetic Sequence 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.

Formula of Arithmetic Sequence

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

Arithmetic Sequence Formula
nth Term Formula an = a1 + (n – 1)d

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

Some solved problems on arithmetic sequence are given below:

Solved Examples

Question 1: Find the 16th term in the 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 $\times$ 2)
a16 = 0 + 30
a16 = 30


Practise This Question

A choke coil is preferred to a rheostat in ac circuit as