Arithmetic Sequence Calculator

This is why it also goes by the name nth term calculator. In addition to finding the nth term, you can also use it to find the sum of the series.

How to use this arithmetic sequence calculator?

To find the nth term and sum of the arithmetic sequence through this calculator, you will have to:

1. Enter the nth term (the term you want to find).
2. Enter the first term of the sequence.
3. Input the common difference of the progression.
4. Click calculate.

What are arithmetic progression and nth term?

Arithmetic progression is defined as a sequence 
   “When the distance between consecutive terms is constant. It depends on the common difference(d).”
For example; a sequence is 2,4,6,8,... In this sequence, each term is two numbers bigger than the previous one. 6 is bigger than 4 by 2 digits. Similarly, 8 is greater than 6 by 2 digits.
The common difference is 2 and the sequence is an arithmetic sequence. 
The nth term is an unknown term in an arithmetic sequence.

Nth term and the sum of the series formulas:

There is a formula used to find the value of any place in a sequence. This formula is;

Nth term = a1 + (n-1)d

In this equation 

• A1 ----> First term of the sequence.
• n -----> unknown term’s place.
• d -----> common difference.

The formula to find what is the total sum of all the entries of a sequence from 1st entry to the nth term is;

Sum of series = n/2 [2a1 + (n-1)d]

Or you can find each term separately and add them.

Did you know? The entries of a series are separated by the plus (+) sign while in sequence entries are separated by commas (,). 

How to find the nth term in an arithmetic sequence?

Identify the first value from the sequence. Subtract two consecutive terms to find the value of d. Put all of these values in the formula and simplify.

OR you can use a shortcut aka arithmetic sequence calculator. Also, try the geometric progression calculator.

Example:

For the following sequence, find the value of the 10th term.
15, 18, 21, 24, 27, … 
Also, find the arithmetic series and its sum for this sequence.

Solution:

Step 1: Identify the values.

First value = 15 
Common difference = 18 - 15 = 3
Nth term = 10th term

Step 2: Put the values in the formula. 

Nth term = a1 + (n-1)d
Nth term = (15) + (10-1)(3)
Nth term = 15 + (9)(3)
Nth term = 15 + 27 
Nth term = 42

Step 3: Find all the terms and add them.

a1 = 15 
a2 = a1 + d = 15 + 3 = 18
a3 = a2 + d = 18 + 3 = 21
a4 = a3 + d = 21 + 3 = 24
a5 = a4 + d = 24 + 3 = 27
a6 = a5 + d = 27 + 3 = 30
a7 = a6 + d = 30 + 3 = 33
a8 = a7 + d = 33 + 3 = 36
a9 = a8 + d = 36 + 3 = 39
a10 = a9 + d = 39 + 3 = 42

Sum of the series = 18 + 21 + 24 + 27 + 30 + 33 + 36 + 39 + 42
Sum of the series = 285