Increase of +2
20th term x 2 = 40
(take away the first 4 terms)
40 - (4 x 2) = 32
By formula method:
This is an arithmetic progression.
First term is a = --6; common difference d = +2 the expected term n = 20
By formula, tn = a + (n--1)d
Hence plugging, the required 20th term is --6 + 38 = 32
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As can be seen, each succesive term is 2 greater than the last. We can write a rule to calculate the nth term. Here the rule equals 2n - 8. So the 20th term = (2 * 20) - 8 = 32.
If the Fibonacci sequence is denoted by F(n), where n is the first term in the sequence then the following equation obtains for n = 0.
It is the sequence of first differences. If these are all the same (but not 0), then the original sequence is a linear arithmetic sequence. That is, a sequence whose nth term is of the form t(n) = an + b
To find the nth term of a sequence, we first need to identify the pattern or rule governing the sequence. In this case, the sequence appears to be increasing by 4, then 8, then 12, then 16, and so on. This pattern suggests that the nth term can be represented by the formula n^2 + n, where n is the position of the term in the sequence. So, the nth term for the given sequence is n^2 + n.
To find the nth term of a sequence, we first need to identify the pattern or rule governing the sequence. In this case, the sequence appears to be increasing by 9, then 13, then 17, and so on. This pattern indicates that the nth term is given by the formula n^2 + n - 1. So, the nth term of the sequence 0, 9, 22, 39, 60 is n^2 + n - 1.