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To find the nth term of a sequence, we first need to determine the pattern or rule that governs the sequence. In this case, the sequence appears to be increasing by adding consecutive odd numbers: 3, 6, 9, 12, and so on. Therefore, the nth term formula for this sequence is Tn = 3n^2 + n. So, the nth term for the sequence 4, 7, 13, 22, 34 is Tn = 3n^2 + n.
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It is T(n) = n2 + 4*n + 2.
It means the sum of all 5 numbers divided by 5 is 34, which is equivalent to the sum of all five numbers is 170, 5(34). There are many possibilities for 5 numbers to have a sum of 170. It's good if those numbers are close to the mean, 34. For example, 32 + 33 + 34 + 35 + 36 = 170.
(1/sq rt 5)((1+sq rt 5)/2)n - (1/sq rt 5)((1-sq rt 5)/2)n This is based on the golden ratio (1+sq rt 5)/2) because the ratio of 2 Fibonacci terms approaches the golden ratio as the 2 terms used get larger. IE the ratio ot the 10th term to the 9th term is 55/34 = 1.61765 and the golden ratio is approx. 1.61803. When using this formula if your calculator does not round, you will round to get the appropriate Fibonacci number.