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The rule for the sequence is an = xn-1 + xn-2The sequence of numbers, 1, 1, 2, 3, 5, 8, 13, . . . , in which each successive number is equal to the sum of the two preceding numbers.
Those are the first four prime numbers.
1 2 3 4 5 2 5 8 11 14 ... If this is the sequence, the position-to-term rule is 3n-1. However, it could be another sequence depending on the rest of the terms.
The rule for this sequence appears to be adding consecutive prime numbers. The sequence starts with 3, then adds the next prime number 2 to get 4. It then adds 3 (the next prime number) to 4 to get 7, then 5 to 7 to get 12, and so on. Each number in the sequence is the sum of the previous number and the next prime number in order.
It is not possible to give a conclusive answer because for a recursive relationship of order 1, the first (or 0th) term must be specified.A(n) = (5*n^2 + 3*n + 2*A(1) - 8)/2 for n = 1, 2, 3, ...