The sequence is too short for a definitive answer.
One possibility is
Un = n2 - 2n + 2 for n = 1, 2, 3, ...
another is
Un = (n3 - n + 6)/6
or
Un = (n3 - 3n2 + 5)/3
There are many more.
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.
1, 4, 7, 10, 13, …
x1=0 x2=1 for i > 2, xi= xi-1 + xi-2
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 phrase "first difference" is usually associated with a sequence of numbers: a(1), a(2), a(3), a(4), ... . The sequence may have a simple rule for generating the numbers , a complicated rule or, if it is a random sequence, no rule at all.The sequence of first differences is a(2)-a(1), a(3)-a(2), a(4)-a(3), ...
the rule is:keep adding double starting from 1
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.
1, 4, 7, 10, 13, …
It suggests that it is '2' to a given power/index number/ exponential. 1 = 2^(0) 2 = 2^(1) 4 = 2^(2) Then 2^(3) = 8 2^(4) = 16 et seq. When the power is less than '0' 2^(-1) = 1/2^(1) = 1/2 ( 0.5) 2^(-2) = 1 / 2^(2) = 1/4 (0.25) 2^(-3) = 1/2^(3) = 1/8 = ( 0.125) et seq.
x1=0 x2=1 for i > 2, xi= xi-1 + xi-2
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 phrase "first difference" is usually associated with a sequence of numbers: a(1), a(2), a(3), a(4), ... . The sequence may have a simple rule for generating the numbers , a complicated rule or, if it is a random sequence, no rule at all.The sequence of first differences is a(2)-a(1), a(3)-a(2), a(4)-a(3), ...
3n - 7
Without further terms in the sequence, it is impossible to determine what the rule in the sequence is.
The sequence 1, 8, 27, 64 represents the cubes of the natural numbers 1, 2, 3, and 4 respectively. In mathematical terms, this sequence follows the rule of n^3, where n represents the position of the number in the sequence. Therefore, the rule for this sequence is n^3, where n starts at 1 and increments by 1 for each subsequent number.
Lucas sequences are sequences of numbers which are defined by two seeds: U(1) and U(2); and an iteration rule: U(n+2) = U(n) + U(n+1) for n = 1, 2, 3, ... When the two seeds are both 1, the sequence is the well known Fibonacci sequence.
It is Un = 3n - 7.