Mathematics
lolz345
16

find the nth term in the sequence -6,-3,0,3,6

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(1) Answers
Lizmin

First, determine what type of sequence the set of numbers make up. Through simple logic, it is an arithmetic sequence, because one can see by inspection that there is a common difference of 3 (positive 3, just to be a bit more pedantic). We then use the formula, [latex] t_{n} = a + (n - 1)d[/latex] where [latex] t_{n} [/latex] represents the [latex] n^{th} [/latex] term; a represents the starting term (so the first number in the set of numbers, which in this case is -6); n is the term number (1st, 2nd, 3rd term, etc.); d is the common difference, that is, when you subtract the next term to the previous term – what is that numerical value. To elaborate a bit more, your 1st term is -6, 2nd is -3, 3rd is 0, etc. Also, the formula above is something you just learn, unless you learn to proof this formula, which is something different. So, here, [latex] t_{n} = -6 + (n-1)3[/latex], which can be expanded to: [latex] t_{n} = -6 + 3n-3[/latex] Therefore, [latex] t_{n} = 3n - 9[/latex]

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