Q: What is the rule to the sequence of - 2 3 8 13 18 23 28 33 and 38?

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The 'n'th term is [ 13 + 5n ].

By figuring out the rule on which the sequence is based. I am pretty sure the last number is supposed to be 125 - in that case, this is the sequence of cubic numbers: 13, 23, 33, etc.

(13 + 23)/2 = 18

13 - 14 - 18 - 23 - 32 = -74

A simple answer, based on a linear rule is U(n) = 5n - 23 for n = 1, 2, 3, ...

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Every next number is increased by 5. The next number in the sequence is 23.

8, 13, 18, 23, 28, etc.

The 'n'th term is [ 13 + 5n ].

The 'n'th term is [ 13 + 5n ].

The 'n'th term is [ 13 + 5n ].

By figuring out the rule on which the sequence is based. I am pretty sure the last number is supposed to be 125 - in that case, this is the sequence of cubic numbers: 13, 23, 33, etc.

Since the terms of the given sequence differ by different numbers, then the terms would start a new pattern, so that the other term of the sequence is 23.16 26 21 13 23 18 10...

18,23,28,33,... #1 is 18 #2 is 23 A difference of '5' Hence we can write '5n + x = 18 Where 'n' equals '1' Hence 5(1) + x = 18 5 + x = 18 Hence x = 18 - 5 = 13 So nth term is 5n + 13 NB Verification; does it work for the 4th term 5(4)+ 13 = 20 + 13 = 33 Which is true from above list.

The next number in the sequence would be 23. The sequence consists of prime numbers.

(13 + 23)/2 = 18

By subtracting one term from the next the common difference can be found: Using -8 and -13: -13 - -8 = 13 + 8 = -5 → Common difference is -5.

It is T(n) = n2 + 4*n + 2.