The common difference (d) between successive terms is -9.
The first term (a) is 26
The formula for the nth term [a(n)] of an Arithmetic Series is , a + (n - 1)d.
Inputting the values for a and d gives :-
a(n) = 26 - 9(n - 1) = 26 - 9n + 9 = 35 - 9n......where n = 1,2,3......
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It is: nth term = 35-9n
It is: 26-6n
To find the nth term of this sequence, we first need to determine the pattern or rule governing the sequence. By examining the differences between consecutive terms, we can see that the sequence is increasing by 9, 15, 21, 27, and so on. This indicates that the nth term is given by the formula n^2 + 1.
Look at the differences bettween the terms: 9-2=7, 5-9=-4, 13-5=8, 10-13=-3The differences finally are: 7,-4,8-3,9,-2. The next difference must be 10, so the next term is 27(27-17=10) and the next difference must be -1, so the next term must be 26(26-27=-1). Finally, the sequence is: 2 9 5 13 10 19 17 27 26 and so on.
The sequence S = 2, 2, 4, 6, 10, 16, 26, ... is the Fibonacci sequence multiplied by 2. Like the Fibonacci sequence, each term is found by adding the two previous terms, so Sn = Sn-1 + Sn-2.