Well, darling, the common difference in that sequence is a sassy 8. You see, each number jumps up by 8 from the previous one, making it a piece of cake to figure out. So, go ahead and flaunt your math skills with that knowledge!
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A common difference is a mathematical concept that appears in arithmetic sequences. An arithmetic sequence is a sequence of numbers, U(1), U(2), ... generated by the following rule: U(1) = a U(2) = U(1) + d U(3) = U(2) + d and, in general, U(n) = U(n-1) + d that is, you have a starting number a and, after that, each term in the sequence is found by adding a fixed number, d, to the previous term in the sequence. An equivalent formulation is U(n) = a + (n-1)*d The difference between any two consecutive terms is d and this is the common difference. For example, in the sequence 3, 7, 11, 15, 19, .... the common difference is 4. This is because 7-3 = 4 11-7 = 4 15-11 = 4 and so on.
Well, honey, looks like we've got ourselves an arithmetic sequence here with a common difference of 7. So, to find the nth term, we use the formula a_n = a_1 + (n-1)d. Plug in the values a_1 = 12, d = 7, and n to get the nth term. Math doesn't have to be a drag, darling!
11 and 19 are prime numbers so only common factor is 1.
The nth term in this sequence is 4n + 3.