Find the first term of an arithmetic sequence calculator

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Solve arithmetic progressions step by step

The calculator will find the terms, common difference and sum of the first $$$n$$$ terms of the arithmetic sequence from the given data, with steps shown.

Related calculator: Geometric Sequence Calculator

Your Input

Find $$$a_{7}$$$, $$$S_{15}$$$, given $$$a_{1} = 5$$$, $$$d = 2$$$.

Solution

We have that $$$a_{1} = 5$$$.

We have that $$$d = 2$$$.

$$$a_{7} = a_{1} + d \left(7 - 1\right) = 5 + 2 \left(7 - 1\right) = 17$$$

$$$S_{15} = \frac{2 a_{1} + d \left(15 - 1\right)}{2} \cdot 15 = \frac{\left(2\right)\cdot \left(5\right) + 2 \left(15 - 1\right)}{2} \cdot 15 = 285$$$

Answer

$$$a_{7} = 17$$$A

$$$S_{15} = 285$$$A

Arithmetic progression

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Disp-Num

[1]  2022/09/07 22:29   40 years old level / A homemaker / Useful /

[2]  2022/09/07 02:36   Under 20 years old / Elementary school/ Junior high-school student / Very /

[3]  2022/05/02 17:42   Under 20 years old / High-school/ University/ Grad student / Very /

[4]  2021/07/28 12:07   Under 20 years old / High-school/ University/ Grad student / Useful /

[5]  2021/07/07 00:30   Under 20 years old / High-school/ University/ Grad student / Very /

[6]  2021/02/03 15:02   20 years old level / Others / Very /

[7]  2021/01/21 10:32   Under 20 years old / High-school/ University/ Grad student / Very /

[8]  2020/08/17 12:17   Under 20 years old / High-school/ University/ Grad student / Very /

[9]  2020/08/12 13:57   40 years old level / An engineer / Very /

[10]  2020/04/19 11:36   20 years old level / High-school/ University/ Grad student / Useful /

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Arithmetic Sequence Calculator helps to calculate the first five terms in an arithmetic progression. If a set of numbers follows a specific sequence it is known as a progression.

What is Arithmetic Sequence Calculator?

Arithmetic Sequence Calculator is an online tool that helps to compute the first five terms of an arithmetic progression when the first term and the common difference are known. To use the arithmetic sequence calculator, enter the values in the given input boxes.

Arithmetic Sequence Calculator

NOTE: Please enter the values up to three digits only.

How to Use Arithmetic Sequence Calculator?

Please follow the steps below to find the terms in an arithmetic progression using the arithmetic sequence calculator:

• Step 1: Go to Cuemath's online arithmetic sequence calculator.
• Step 2: Enter the first term(a), and the common difference(d) in the given input boxes of the arithmetic sequence calculator.
• Step 3: Click on the "Find" button to find the terms in the arithmetic sequence.
• Step 4: Click on the "Reset" button to clear the fields and enter new values.

How Does Arithmetic Sequence Calculator Work?

An arithmetic progression (AP) can be defined as a sequence where the difference between two consecutive terms is the same. In an AP new terms can be obtained by adding a fixed number to its previous term. There can be many types of progressions in mathematics such as geometric progressions and harmonic progressions. The terms of an AP follow the sequence given below:

AP = a, a + d, a + 2d, a + 3d, a + 4d, .....

Here, a denotes the first term of the AP while d is the common difference between two successive terms.

The nth term of an AP is given by a general representation as follows:

an = a + (n - 1)d.

The steps to find the different terms of an AP, if we know the first term and the common difference, are given below:

• Write the first term as it is; a
• Add the common difference to the first term to get the second term; a + d.
• To get the third term, add the common difference to the second term. Thus, (a + d) + d = a + 2d.
• Similarly, the fourth term can be obtained by adding the common difference to the third term; a + 2d + d = a + 3d.
• Continue this process till the desired number of terms in the AP have been determined.

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Solved Examples on Arithmetic Sequence

Example 1: Find the arithmetic sequence up to 5 terms if the first term(a) = 6, and common difference(d) = 7. Verify the result using the arithmetic sequence calculator.

Solution:

Given: a = 6, d = 7

an = a + (n - 1)d

a1(first term) = 6 + (1 - 1)7 = 6 + 0 = 6

a2(second term) = 6 + (2 - 1)7 = 6 + 7 = 13

a3(third term) = 6 + (3 - 1)7 = 6 + 14 = 20

a4(fourth term) = 6 + (4 - 1)7 = 6 + 21 = 27

a5(fifth term) = 6 + (5 - 1)7 = 6 + 28 = 34

Therefore, the arithmetic sequence is {6, 13, 20, 27, 34 ...}

Example 2: Find the arithmetic sequence up to 5 terms if the first term(a) = 2.5, and common difference(d) = 1.1. Verify the result using the arithmetic sequence calculator.

Solution:

Given: a = 2.5, d = 1.1

an = a + (n - 1)d

a1(first term) = 2.5 + (1 - 1)1.1 = 2.5 + 0 = 2.5

a2(second term) = 2.5 + (2 - 1)1.1 = 2.5 + 1.1 = 3.6

a3(third term) = 2.5 + (3 - 1)1.1 = 2.5 + 2.2 = 4.7

a4(fourth term) = 2.5 + (4 - 1)1.1 = 2.5 + 3.3 = 5.8

a5(fifth term) = 2.5 + (5 - 1)1.1 = 2.5 + 4.4 = 6.9

Therefore, the arithmetic sequence is {2.5, 3.6, 4.7, 5.8, 6.9, ...}

Similarly, you can try the arithmetic sequence calculator to find the terms of the arithmetic progression for the following:

• First term(a) = 5, common difference(d) = 10
• First term(a) = 4.9, common difference(d) = 2.3

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