A sequence is referred as a set of numbers with a predefined order. These numbers are separated by commas. **For example:**

- 1, 4, 9, 16, 25, ....
- 5, 10, 15, 20, 25, ....

In mathematics, series is the sum of a finite sequence or we can say that it is a sum of few terms of a sequence.

In arithmetic sequence or arithmetic progression, the difference between two consecutive numbers always remains same.

- 1, 3, 5, 7, 9, .... where difference between 3 and 1, 5 and 3, 7and 5, 9 and 7 are all equal to 2.
- 100, 97, 94, 91, .... where 97 -100 = 94 - 97 = 91 - 94 = - 3

Arithmetic series is the sum of the finite terms of an arithmetic sequence, i.e. the sum of n number of terms of an arithmetic sequence is known as arithmetic series. When addition symbol (+) is used to separate every two consecutive numbers of an arithmetic sequence, it becomes arithmetic series.

- 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21
- 100 + 97 + 94 + 91 + 88

$S_{n}=$$\frac{n}{2}$$(a+a_{n})$

Where,n = Total number of terms

$S_{n}$ = Sum of first n terms

a = First term

$a_{n}$ = Last term

$S_{n}=$$\frac{n}{2}$$[2a+(n-1)d]$

Where,a = First term

d = Common difference

n = Total number of terms

$S_{n}$ = Sum of first n terms

and d = 7 - 4 = 10 - 7 = 3

Let us use the formula

$S_{n}=$$\frac{n}{2}$$[2a+(n-1)d]$

$S_{10}=$$\frac{10}{2}$$[2 \times 4 +(10-1) \times 3]$

$S_{10}=5 \times(8 + 27)$

Required sum = 175

Related Calculators | |

Arithmetic Series Calculator | Arithmetic Calculator |

Arithmetic Mean Calculator | Mod Arithmetic Calculator |