Arithmetic Sequence Calculator

In order to know about Arithmetic Sequence firstly, you need to know what a sequence actually means. A sequence is defined as the ordered list of numbers. Each and every number in a sequence is referred to as the term. Arithmetic Sequence is a set of objects more specific numbers. Each consecutive number is obtained a constant number i.e. common difference to the previous one. The Sequence can be finite if you have determined the number of terms and infinite if the number of terms isn't specified.

Arithmetic Sequence is defined by two coefficients namely common difference and first term. If you know these two values you can write down the entire sequence.

Let's assume you want to find the 30th term of a sequence. Writing all the 30 terms can be quite tedious and time-consuming. On a generalized note, it is enough if you add the 29 common differences to the first term.

The formula for Arithmetic Sequence Equation is given as follows. Check out the formula for the nth term of a sequence.

a = a₁+(n-1)d

where a is the nth term of the sequence

d is the common difference

a₁ is the first term of the sequence

The Arithmetic Sequence formula listed above is applicable in the case of all common differences be it positive or negative. In the case of a zero difference, all the numbers are equal and no further calculations are needed.

Want to know the summation of Arithmetic Sequence? Trust us it's not going to be hard and you can do it on your own. In order to find the summation of a sequence all you have to do is add the first and last term of the sequence and multiply them with the number of pairs.

Mathematically, S = n/2 * (a₁ + a)

Substitute the value of Arithmetic Sequence of nth term we get

S = n/2 * [a₁ + a₁ + (n-1)d]

After simplification,

S = n/2 * [2a₁ + (n-1)d]

By this formula, you can find the Summation of Arithmetic Sequence easily.

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