Sum of a Linear Number Sequence Calculator

FAQs

What is the formula for the sum of a linear sequence?

The formula for the sum of a linear sequence reads: sum = n / 2 × (2 × a + diff × (n - 1)) where: a is the initial value of the sequence; diff is the difference between any two consecutive numbers is your sequence; n is the number of periods (of elements in your sequence); and sum is the sum you're looking for.

How do I find the sum of a linear sequence?

To compute the sum of a linear sequence: Write down the initial value of your sequence a. Compute the final value of your sequence as a + diff × (n - 1), where diff is the difference of your sequence, and n is the number of its elements. Add together the results of Step 1 and Step 2. Multiply the result by n. Divide the result by 2. That's it!

How do I find the final value of a linear sequence?

To determine the final value of a linear sequence: Write down the initial value a of your sequence as well as the difference diff between the two consecutive steps. Decide how many elements you want in your sequence. Denote this value by n. Compute diff × (n - 1). Add a to the number obtained in Step 3. This is your result: the value of the final, i.e., the nth element of your linear sequence.

Are linear sequences and arithmetic sequences the same?

Yes, the terms linear sequence and arithmetic sequence describe the same type of sequences: those that arise by always adding the same amount to the previous value to get the next value. This amount is called the difference of the linear/arithmetic sequence.

What is the sum of the first 100 numbers?

The answer is 5050. This is because the natural numbers form a linear sequence of n = 100 elements with the initial value a = 1 and the difference of diff = 1. Applying the formula for the sum of linear sequence, we get sum = n / 2 × (2 × a + diff × (n - 1)) = 100 / 2 × (2 × 1 + 1 × (100 - 1)). It follows easily that sum = 5050.