Use the free online Arithmetic Sequence Calculator tool to find nth term of sequence and the sum of the arithmetic sequence and n terms of progression.
A sequence is a list of numbers in a particular order. Each number in a sequence is called a term. The first term is represented by a1, the second term is represented by a2 , and so on. an represents the nth term of the sequence. One kind of sequence is an arithmetic sequence. In an arithmetic sequence each term after the first is found by adding a constant, called the common difference, d, to the previous term.
A simple way to generate a sequence is to start with a number a, and add to it a fixed constant d, over and over again. This type of sequence is called an arithmetic sequence.
An arithmetic sequence is a sequence of the form: a, a + d, a + 2d, a + 3d, a + 4d, ........
The number a is the first term, and d is the common difference of the sequence.
The nth term of an arithmetic sequence is given by: an = a1 + (n – 1)d
The number d is called the common difference because any two consecutive terms of an arithmetic sequence differ by d, and it is found by subtracting any pair of terms an and an+1.
That is: d = an+1 – an
To find a formula for the sum, Sn, of the first n terms of an arithmetic sequence, we can write out the terms as
Sn = a + (a+d) + (a+2d) +......+[a+(n-1)d]
The final equation of Sum of arithmetic sequence is: Sn = n/2(a + an)
Example: Find the nth term, the fifth term, and the 100th term, of the arithmetic sequence determined by a = 2 and d = 3.
Solution: To find a specific term of an arithmetic sequence, we use the formula for finding the nth term. The nth term of an arithmetic sequence is given by an = a + (n – 1)d.
So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula.
an = 2 + (n – 1)3
Now, to find the fifth term, substitute n = 5 into the equation for the nth term.
a5 = 2 + (5 – 1)3 = 14
Finally, find the 100th term in the same way as the fifth term.
a100 = 2 + (100 – 1)3 = 299
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