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.
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It is: nth term = 35-9n
It is: 26-6n
To find the nth term of the sequence 11, 21, 35, 53, 75, 101, we can observe the differences between consecutive terms: 10, 14, 18, 22, and 26, which increase by 4 each time. This suggests that the sequence can be described by a quadratic function. The nth term can be represented as ( a_n = 5n^2 + 6n ), where n starts from 1. Thus, the nth term corresponds to this formula for values of n.
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......
107 ÷ 26 = 4 with remainder 3