gauss sequence formula
The formula for a Gauss sequence is: a_n = a_1 + (n-1)d, where a_1 is the first term in the sequence, n is the nth term in the sequence, and d is the common difference between consecutive terms.
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Sn = n/2 (a_1 + a_n)
The formula for the sum of a Gauss sequence is:
S = n/2(a + l)
where:
- S is the sum of the sequence
- n is the number of terms in the sequence
- a is the first term of the sequence
- l is the last term of the sequence
The Gauss sequence formula, also known as the arithmetic sequence formula, is used to find the nth term in an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.
The Gauss sequence formula is given by:
an = a1 + (n - 1)d
where:
- an represents the nth term in the sequence
- a1 represents the first term in the sequence
- n represents the position of the term you want to find
- d represents the common difference between consecutive terms
To use the Gauss sequence formula, you need to know the first term (a1) and the common difference (d). Once you have these values, you can substitute them into the formula to find the desired term (an).
Here is an example to illustrate how to use the Gauss sequence formula:
Consider an arithmetic sequence with a first term of 3 and a common difference of 2. We want to find the 7th term in this sequence.
Using the formula:
a7 = a1 + (n - 1)d
Substituting the known values:
a7 = 3 + (7 - 1) * 2
Calculating:
a7 = 3 + 6 * 2
= 3 + 12
= 15
Therefore, the 7th term in this arithmetic sequence is 15.
Remember to always check your calculations and validate your results to ensure accuracy.