# Sequence and Series Formulas

**Sequence and Series Formulas**

A sequence is a ordered list of numbers and series is the sum of the term of sequence.

Some of the important formulas of sequence and series are given below:-

**Arithmetic Series**

1. *For the numbers in arithmetic progression*,

N’th terms:

Where a = first terms, d = common difference.

N’th mean:

2. *For the arithmetic series*,

The last term

The sum,

3. *Sum of squares of n natural numbers*

4. *Sum of cubes of n natural numbers*

5. *For the numbers in geometric progression*,

N’th term: and n’th mean,

**Geometric Series**

1. *For the geometric series, the sum*

if r > 1, if r < 1

if, r < 1, if n is very large,

2. *For any two numbers a and b.*

if , if a = b

3.* Mean*

i. a. *Arithmetic mean* (A.M.) =

b. For more arithmetic means “d” is to be found as then,

mean

Where a = first term, b = last term, d = common difference

ii.a. Geometric mean (G.M) =

b. For more geometri means “r” is to be found as

then, mean

Where a = first term, b = last term, r = common ratio.

4. If AM & GM be the A.M. A\and G.M. between two positive numbers and b then .

5. Sum of the first ‘n’ natural numbers ( 1+ +2 +3 + ……………………+ n) is .

6. Sum of the first ‘n’ odd natural numbers (1 + 3 + 5 + ………………………to n terms) is

7. Sum of the first ‘n’ even natural numbers (2 +4 +6 + ……………………….to n terms ) is

8. Sum of squares of the first ‘n’ natural numbers

is .

9. Sum of the cubes of first ‘n’ natural numbers

is .

10.

11.

Related posts:

- Statistics formulas Statistics formulas related to mean , median , quartiles ,...
- Ratio and Proportion Formulas As you know Ratio is a relation between two quantities...
- Algebraic Formulas Algebra is one of the most basic part of mathematics...
- Maths Formulas for Physics Maths Formulas for Physics. List of mathematical formulas used in...
- Simple Interest formulas Interest is a type of fee paid for assets and...