Arithmetic Sequence Calculator

Nth term calculator

This online Arithmetic Sequence Calculator aka nth term calculator is used to find the value of the nth term in an arithmetic progression. 

It is also used as an Arithmetic progression calculator as it finds the sequence for the data provided. You can also see the sum till the nth term.

What is Arithmetic Sequence?

An arithmetic sequence is alternatively called arithmetic progression. It refers to the sequence of numbers where the difference between any two adjacent numbers is the same.

In other words, arithmetic progression is a sequence of numbers such as the positive odd integers 1, 3, 5, 7, …, in which the same number is added to each number to produce the next. 

Arithmetic sequence formula:

The formula of an arithmetic sequence is very simple. It is written in a number of ways but the most common way is:

a_n  = a₁ + (n-1)* d

Where

• a_n is the nth value.
• a₁ is the first term of the progression/sequence.
• n is the required no. of term.
• d is the common difference.

How to find the nth term?

Example: 

Calculate the nth term of the arithmetic progression which has the following set of data. Also, find the sequence till nth term.

last-Term n = 10

First-term a₁= 2

Common difference d = 2

Solution:

Part 1: Finding the nth term.

Put the values in the arithmetic progression formula.

a_n  = a₁ + (n-1)* d

a_n  = (2)+ (10-1)* 2

a_n  = 2+ 18

a_n  = 20

Part 2: Finding the sequence. 

We already know the value of the first and last term. Find the values of the sequence by putting the digits from 2 to 9 in the formula.

a₂  = a₁ + (n-1)* d = (2)+ (2-1)* 2 = 4

a₃  = a₁ + (n-1)* d = (2)+ (3-1)* 2 = 6

a₄  = a₁ + (n-1)* d = (2)+ (4-1)* 2 = 8

a₅  = a₁ + (n-1)* d = (2)+ (5-1)* 2 = 10

a₆  = a₁ + (n-1)* d = (2)+ (6-1)* 2 = 12

a₇  = a₁ + (n-1)* d = (2)+ (7-1)* 2 = 14

a₈  = a₁ + (n-1)* d = (2)+ (8-1)* 2 = 16

a₉  = a₁ + (n-1)* d = (2)+ (9-1)* 2 = 18

Write the sequence till the nth term.

2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20