Find The 70th Term of The Following Arithmetic Sequence Calculator

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This calculator helps you find the 70th term of any arithmetic sequence by using the standard formula for arithmetic sequences.

What is an Arithmetic Sequence?

An arithmetic sequence is a sequence of numbers where the difference between each consecutive term is constant. This difference is known as the common difference, often denoted by 'd'. The first term of the sequence is usually denoted by 'a₁'.

Examples of arithmetic sequences include:

2, 5, 8, 11, 14, ... (common difference of 3)
10, 7, 4, 1, -2, ... (common difference of -3)
3, 3, 3, 3, 3, ... (common difference of 0)

Arithmetic sequences are fundamental in mathematics and appear in various real-world applications, from finance to physics.

The Formula

The nth term of an arithmetic sequence can be found using the following formula:

Arithmetic Sequence Formula

aₙ = a₁ + (n - 1) × d

Where:

aₙ = nth term
a₁ = first term
d = common difference
n = term number

This formula allows you to calculate any term in the sequence once you know the first term and the common difference.

How to Use the Calculator

Using the calculator is straightforward:

Enter the first term (a₁) of your arithmetic sequence.
Enter the common difference (d) between terms.
Click the "Calculate" button to find the 70th term.
The result will be displayed in the result box below the calculator.

The calculator will show you the exact value of the 70th term based on the inputs you provide.

Worked Example

Let's find the 70th term of the arithmetic sequence where the first term is 5 and the common difference is 3.

Example Calculation

Given:

a₁ = 5
d = 3
n = 70

Using the formula:

a₇₀ = 5 + (70 - 1) × 3

a₇₀ = 5 + 69 × 3

a₇₀ = 5 + 207

a₇₀ = 212

The 70th term of this sequence is 212.

FAQ

What is the difference between an arithmetic sequence and a geometric sequence?: An arithmetic sequence has a constant difference between terms, while a geometric sequence has a constant ratio between terms.
Can the common difference be negative?: Yes, the common difference can be negative, which results in a decreasing arithmetic sequence.
What if the common difference is zero?: If the common difference is zero, all terms in the sequence are the same, creating a constant sequence.
How can I verify the result from the calculator?: You can verify the result by plugging the values into the arithmetic sequence formula manually or using a different calculator.
Is this calculator free to use?: Yes, this calculator is free to use and does not require any registration or payment.