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Arithmetic Sequence Formula

Arithmetic Sequence is a sequence in which each term is obtained by adding or subtracting a common number to its preceding term. In other words, the difference between the adjacent terms in the arithmetic sequence is the same.

The Arithmetic Sequence Formula is given as,

Where,
an - nth term that has to be found
a1 - 1st term in the series
d - common difference

 Related Calculators Arithmetic Sequence Calculator Arithmetic Calculator Sequence Calculator Arithmetic Mean Calculator

Arithmetic Sequence Problems

Some solved problems on arithmetic sequence are given below:

Solved Examples

Question 1: Find the 13th term in the arithmetic sequence 1, 4, 7, 11, 15,.... ?
Solution:

The arithmetic sequence is given as,
an = a1 + (n - 1)d
From the given problem,
a1 = 1 ; n = 13 ; d = 3
a13 = 1 + (13 - 1)3
a13 = 1 + (12 $\times$ 3)
a13 = 1 + 36
a13 = 37

Question 2: Find the 7th term in the arithmetic sequence 0, 5, 10, 15,.... ?
Solution:

The arithmetic sequence is given as,
an = a1 + (n - 1)d
From the given problem,
a1 = 0 ; n = 7 ; d = 5
a7 = 0 + (7 - 1)5
a7 = 0 + (6 $\times$ 5)
a7 = 0 + 30
a7 = 30

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