This is what might be described as a two-step sequence or two sequences spliced together.
t1 = 1
tn = - (tn-1 +1) for n = 2,4,6, ...
and tn = tn-2 + 3 for n = 3,5,7, ...
i0 = 4; in = in-1 - 3
The rule is multiply the previous term by -1 to find the next term.
The pattern will be +2, +3, +4, +4
add 4 to every other number 1(+4)=5, 5(+4)=9 2(+4)=6
3 is the answer
i0 = 4; in = in-1 - 3
Double the previous number
t(n) = 3(n-1) + 1, for n = 1, 2, 3, etc
The rule is multiply the previous term by -1 to find the next term.
The pattern will be +2, +3, +4, +4
add 4 to every other number 1(+4)=5, 5(+4)=9 2(+4)=6
+2, +3, +2
3 is the answer
2 squared 1 = 4 so the divisibility rule is that it is divisible by 1, 2 and 4.
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.
5-30-6-42-7-56-8-72
Add the increasing numbers by one - as in 0 1 2 3 4 5 6 etc 1 + 0 = 1 1 + 1 = 2 2 + 2 = 4 4 + 3 = 7 7 + 4 = 11 11 + 5 = 16 16 + 6 = 22