Arithmetic sequences is a part of syllabus in algebra 1 (second math course), which finds application in many algebra questions including algebra word problems. An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers, whose consecutive numbers differ by a constant. When n terms of an arithmetic sequence are added, you get arithmetic series. Arithmetic series formula is given by : sum = n/2 (a + l) where a is the 1st term and l is the last term. Learn more about Arithmetic sequences using the resources on this page.

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Recursive formula: This sequence is neither arithmetic nor geometric. It does, however, have a pattern of development based upon each previous term. Notice how the value of n is used as the exponent for the value (-1).

Imagine we want to find a formula for the nth term of this sequence: 7, 11, 15, 19, 23, … We can see that the terms in this sequence go up by 4 each time, so 4n must appear in the formula. The sequence generated by the formula 4n is the four times table, but it isn’t quite the sequence we want: 4n sequence:

A recursive formula designates the starting term, a1, and the nth term of the sequence, an , as an expression containing the previous term (the term before it), an-1. The process of recursion can be thought of as climbing a ladder.

To find the common ratio, divide the second term by the first term. Notice the non-linear nature of the scatter plot of the terms of a geometric sequence. The domain consists of the counting numbers 1, 2, 3, 4, … and the range consists of the terms of the sequence.