Sum of a Linear Number Sequence Calculator
Calculate sum using first term, last term, and number of terms
How to Use This Calculator
Enter First Term
Input the first term (a₁) of your linear number sequence.
Enter Last Term
Input the last term (aₙ) of your sequence.
Enter Number of Terms
Input the total number of terms (n) in your sequence. Must be a positive integer.
Calculate
Click "Calculate Sum" to see the result.
Formula
S_n = n/2 × (a₁ + aₙ)
Where:
- S_n = sum of n terms
- a₁ = first term
- aₙ = last term
- n = number of terms
Example: Sum of 2 + 5 + 8 + 11 + 14 + 17 + 20
a₁ = 2, aₙ = 20, n = 7
S₇ = 7/2 × (2 + 20) = 7/2 × 22 = 77
About Sum of a Linear Number Sequence Calculator
A linear number sequence is an arithmetic sequence where each term increases (or decreases) by a constant amount. This calculator finds the sum of such sequences using the simple formula that requires only the first term, last term, and number of terms.
Key Advantages
- Simple Formula: No need to know the common difference
- Fast Calculation: Only requires first term, last term, and count
- Perfect for Arithmetic Sequences: Works with any linear sequence
Common Applications
- Summing consecutive numbers
- Calculating totals in arithmetic progressions
- Quick calculations when you know the endpoints
Frequently Asked Questions
What is a linear number sequence?
A linear number sequence is an arithmetic sequence where terms increase or decrease by a constant amount. Example: 2, 5, 8, 11, 14, ...
Do I need to know the common difference?
No! This formula only requires the first term, last term, and number of terms. The common difference doesn't need to be known.
Can I use this for decreasing sequences?
Yes! The formula works for both increasing and decreasing sequences. Just make sure the last term is the actual final term in your sequence.
What if the sequence doesn't start at 1?
The formula works for any starting value. Just use the actual first term, not the position number.
How is this different from the arithmetic series formula?
This is an alternative formula. Instead of S_n = n/2 × [2a₁ + (n-1)d], we use S_n = n/2 × (a₁ + aₙ), which doesn't require knowing the common difference d.