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# Sum of a Linear Number Sequence Calculator

To use this calculator, select the sequence, enter the values, and click calculate button

## Sum of a Linear Number Sequence Calculator

Sum of a Linear Number Sequence Calculator is used to find the Arithmetic sequence and Geometric sequence. These sequence series find out by entering the first term, a common difference of series, and also entering the n^{th} term of the sequence.

## Arithmetic sequence:

The Arithmetic sequence is a series of numbers that is found by adding the common difference in the previous term.

**Example:**

The given set of series {2, 5, 8, 11, 14, ...} is an arithmetic series of numbers with a common difference of number “3”. To find the next term in the sequence add the “3” in the previous term and get the answer “**17**” such as “14 + 3 = 17”.

### Formula of Arithmetic sequence

The “n^{th} term” formula of an Arithmetic sequence is stated as.

**a _{n} = a_{1} + (n - 1)d**

Where,

- a
_{1}= first term - d = common difference
- n = number of terms that finds

## Geometric sequence:

It is a set of values that are the first term's multiple and the common ratio to the power of the nth term. In other words, it’s finding the process of terms one by one using any algebraic technique.

**Example:**

The given set of series {2, 4, 8, 16, 32, ...} is a geometric series of numbers with a common multiple ratio “2”. To evaluate the next term in the sequence multiply 2*2^{(6-1) }= 64.

### Formula of Geometric sequence:

The “n^{th} term” formula of a geometric sequence is stated as.

**a _{n} = a_{1} × r^{(n-1)}**

Where,

- a
_{1}= first term - r = common multiple ratios
- n = number of terms that finds

## Examples

**Example 1:**

Find the geometric sequence of numbers if the data are given below.

Find the fourth term of the sequence if the first term is 4, and the common difference of numbers is 3.

**Solution:**

**Step 1:**

Write the data.

Total number of term = n = 4, first term = a_{1} = 4, common difference = r = 3.

**Step 2:**

Write the formula of the geometric sequence.

a_{n} = a_{1} × r^{(n-1)}

**Step 3:**

Put the values in the above formula and simplify.

n = 4, a_{1} = 4, r = 3

a_{n} = a_{1} × r^{(n-1)}

**Put n=2, **

a_{2} = 4 × 3^{(2-1)}

a_{2} = 4 × 3^{(1)}

a_{2} = 4 × 3

a_{2} = 12

**Put, n =3,**

a_{3} = 4 × 3^{(3-1)}

a_{3} = 4 × 3^{(2)}

a_{3} = 4 × 9

a_{3} = 36

**Put, n =4,**

a_{4} = 4 × 3^{(4-1)}

a_{4} = 4 × 3^{(3)}

a_{4} = 4 × 27

a_{4} = 108

**Thus the {4, 12, 36, 108} is the geometric sequence and the fourth term is 108.**

**Example 2:**

Find the Arithmetic sequence of numbers if the data are given below.

Find the fourth term of the sequence if the first term is 2, and the common difference of numbers is 4.

**Solution:**

**Step 1:**

Write the data.

Total number of term = n = 4, first term = a_{1} = 2, common difference = d = 4.

**Step 2:**

Write the formula of an Arithmetic sequence.

a_{n} = a_{1} + (n - 1)d

**Step 3:**

Put the values in the above formula and simplify.

n = 4, a_{1} = 2, d = 4

a_{n }= a_{1} + (n - 1)d

**Put n=2, **

a_{2 }= 2 + (2 - 1)4

a_{2} = 2 + (1)4

a_{2} = 2 + 4

a_{2} = 6

**Put, n =3,**

a_{3} = 2 + (3 - 1)4

a_{3} = 2 + (2)4

a_{3} = 2 + 8

a_{3} = 10

**Put, n =4,**

a_{4} = 2 + (4 - 1)4

a_{4} = 2 + (3)4

a_{4} = 2 + 12

a_{4} = 14

**Thus the {2, 6, 10, 14} is the Arithmetic sequence and the fourth term is 14.**