Arithmetic Sequence Formula




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.

Arithmetic Sequence Formula – 
\[\LARGE a_{n}=a_{1}+(n-1)d\]

an – nth term that has to be found
a1 – 1st term in the seriesn
n- number of terms
d – 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….. ?

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 samll bubble rises from the bottom of a lake, where the temperature and pressure are 8C and 6.0 atm, to the water's surface, where the temperature is 25°C and pressure is 1.0 atm. Calculate the final volume of the bubble if its initial volume was 2 mL