-8
arithmetic sequence
An arithmetic sequence.
6
14112027
The sum of the first 12 terms of an arithmetic sequence is: sum = (n/2)(2a + (n - 1)d) = (12/2)(2a + (12 - 1)d) = 6(2a + 11d) = 12a + 66d where a is the first term and d is the common difference.
The difference between succeeding terms in a sequence is called the common difference in an arithmetic sequence, and the common ratio in a geometric sequence.
arithmetic sequence
It is the "common difference".It is the "common difference".It is the "common difference".It is the "common difference".
An arithmetic sequence.
6
29
14112027
The sum of the first 12 terms of an arithmetic sequence is: sum = (n/2)(2a + (n - 1)d) = (12/2)(2a + (12 - 1)d) = 6(2a + 11d) = 12a + 66d where a is the first term and d is the common difference.
If the terms get bigger as you go along, the common difference is positive. If they get smaller, the common difference is negative and if they stay the same then the common difference is 0.
You subtract any two adjacent numbers in the sequence. For example, in the sequence (1, 4, 7, 10, ...), you can subtract 4 - 1, or 7 - 4, or 10 - 7; in any case you will get 3, which is the common difference.
A quadratic sequence is when the difference between two terms changes each step. To find the formula for a quadratic sequence, one must first find the difference between the consecutive terms. Then a second difference must be found by finding the difference between the first consecutive differences.
A sequence of numbers in which the difference between any two consecutive terms is the same is called an arithmetic sequence or arithmetic progression. For example, in the sequence 2, 5, 8, 11, the common difference is 3. This consistent difference allows for predictable patterns and calculations within the sequence.