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, …
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 explicit rule for the sequence 3, 5, 7, 9 can be expressed as ( a_n = 2n + 1 ), where ( n ) starts from 1. In this formula, ( a_n ) represents the nth term of the sequence. The sequence increases by 2 for each subsequent term, starting from 3. Thus, for ( n = 1, 2, 3, 4 ), the terms are 3, 5, 7, and 9, respectively.
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.