Find The Sum 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 sum of such sequences quickly and accurately.

What is an Arithmetic Sequence?

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference, often denoted by 'd'.

For example, the sequence 2, 5, 8, 11, 14 is an arithmetic sequence where the common difference is 3.

The first term of the sequence is usually denoted by 'a₁' or simply 'a'. The nth term of an arithmetic sequence can be found using the formula:

aₙ = a₁ + (n - 1)d

Where:

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

The Formula

The sum of the first n terms of an arithmetic sequence can be calculated using the following formula:

Sₙ = n/2 × (2a₁ + (n - 1)d)

Where:

Sₙ = sum of the first n terms
n = number of terms
a₁ = first term
d = common difference

This formula is derived from the fact that the sum of an arithmetic sequence is the average of the first and last terms multiplied by the number of terms.

How to Use the Calculator

Using our calculator is simple:

Enter the first term (a₁) of your arithmetic sequence
Enter the common difference (d) between terms
Enter the number of terms (n) you want to sum
Click the "Calculate" button

The calculator will display the sum of the sequence and show a visualization of the sequence.

Examples

Example 1

Find the sum of the first 10 terms of the arithmetic sequence where the first term is 3 and the common difference is 2.

Using the formula:

S₁₀ = 10/2 × (2×3 + (10 - 1)×2) S₁₀ = 5 × (6 + 18) S₁₀ = 5 × 24 S₁₀ = 120

The sum of the first 10 terms is 120.

Example 2

Find the sum of the first 5 terms of the arithmetic sequence where the first term is 5 and the common difference is -3.

Using the formula:

S₅ = 5/2 × (2×5 + (5 - 1)×(-3)) S₅ = 2.5 × (10 - 12) S₅ = 2.5 × (-2) S₅ = -5

The sum of the first 5 terms is -5.

FAQ

What is an arithmetic sequence?: An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant.
How do I find the sum of an arithmetic sequence?: You can use the formula Sₙ = n/2 × (2a₁ + (n - 1)d) where n is the number of terms, a₁ is the first term, and d is the common difference.
Can the common difference be negative?: Yes, the common difference can be negative, which means the sequence is decreasing.
What if I only know the first and last terms?: If you know the first and last terms, you can use the formula Sₙ = n/2 × (a₁ + aₙ) where aₙ is the last term.
Is this calculator accurate?: Yes, this calculator uses the standard arithmetic sequence sum formula and performs calculations with high precision.