There are infinitely many possible answers.
One is
Un = (n5 - 10n4 + 55n3 - 110n2 + 184n - 120)/120 for n = 1, 2, 3, ...
Another possible answer is
Un = 2n-1 + 1 for n = 1, 2, 3, ...
Which one of the two? And if you choose one over the other, why did you pick that one and not the other? And why stick to only these two when there are infinitely many to choose from?
33
There is no easy rule for divisibility by 34.
It is not a rule as such; those number are the first 10 prime numbers.
50-16=34 34/2=17 16+17=33 Answer is 33
11205 Pattern rule: Start at 1. Multiply by 7, and subtract 2.
33
One possible answer is: Un = 4n2 - 36n + 89 for n = 1, 2, 3.
The pattern in the sequence 2, 3, 5, 9, 17 can be understood by observing how each number is generated. Each number after the first two is the sum of the two preceding numbers: 2 + 3 = 5, 3 + 5 = 8 (but we have 9), 5 + 9 = 14 (but we have 17). If we continue this pattern, 9 + 17 = 26, and adding the last number (17 + 26) gives us 33, which is the next number in the sequence.
There is no easy rule for divisibility by 34.
Add 3n-1. For example 1 + 30 = 2 2 + 31 = 5 5 + 32 = 14 14 + 33 = 41
To find the number of marbles in the sixth line using the given rule, we start with the first line having 2 marbles. Each subsequent line has a number of marbles that is one less than twice the previous line. Following this pattern: 1st line: 2 2nd line: (2 * 2) - 1 = 3 3rd line: (2 * 3) - 1 = 5 4th line: (2 * 5) - 1 = 9 5th line: (2 * 9) - 1 = 17 6th line: (2 * 17) - 1 = 33 Thus, there must be 33 marbles in the sixth line.
To analyze the pattern, we start with 2 marbles in the first line. According to the rule, each subsequent line has a number that is one less than twice the previous line. Thus, the sequence will be: 1st line: 2 2nd line: (2 \times 2 - 1 = 3) 3rd line: (2 \times 3 - 1 = 5) 4th line: (2 \times 5 - 1 = 9) 5th line: (2 \times 9 - 1 = 17) 6th line: (2 \times 17 - 1 = 33) Therefore, there must be 33 marbles in the sixth line.
There isn't one. * * * * * One possible answer is: Un = 4n2 - 36n + 89 for n = 1, 2, 3.
It is not a rule as such; those number are the first 10 prime numbers.
50-16=34 34/2=17 16+17=33 Answer is 33
11205 Pattern rule: Start at 1. Multiply by 7, and subtract 2.
+2, +3, +2