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Math Help - Write the expression for the nth term

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    Write the expression for the nth term

    Identify the following as arithmetic, geometric, or neither. If the sequence is arithmetic or geometric, write the explicit expression for the nth term.

    a. 1, 3, 5, 7,....
    ~~~ok according to my understanding of the question i have to find the "formula" for this sequence of numbers.. this is what i got:
    2n-1 (n = the 'nth' term)
    ~~~~~~
    b. 4, -6, 9, -13.5,....
    ~~i have no idea how to write an equation for this one..., i was thinking something like (-1)^n-1 for the (+) & (-) changes but i cant figure anything out beyond that...
    ~~~~
    c. 1, x^2, x^4, X^6,....
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by arturju View Post
    Identify the following as arithmetic, geometric, or neither. If the sequence is arithmetic or geometric, write the explicit expression for the nth term.

    a. 1, 3, 5, 7,....
    ~~~ok according to my understanding of the question i have to find the "formula" for this sequence of numbers.. this is what i got:
    2n-1 (n = the 'nth' term)
    ~~~~~~
    b. 4, -6, 9, -13.5,....
    ~~i have no idea how to write an equation for this one..., i was thinking something like (-1)^n-1 for the (+) & (-) changes but i cant figure anything out beyond that...
    ~~~~
    c. 1, x^2, x^4, X^6,....
    you are right for a, but you forgot to ID it as arithmetic, geometric or neither, which do you think it is?

    for (b)
    what is the relationship between the terms? is there a common difference? a common ratio? neither? let's see.

    to go from 4 to -6 you would subtract 10. but subtracting 10 from -6 gives -16, which is not the third term. so there is no common difference.

    what about a common ratio?

    is it true that 6/4 = 9/6 = 13.5/9 ? YES!

    what are these ratios equal to? 6/4 = 9/6 = 13.5/9 = 3/2

    so that is our common ratio, which means this is a geometric sequence.

    so the formula for this sequence will be of the form ar^(n-1), for n = 1,2,3,4,5...

    where a is the first term, r is the common ratio. so obviously, this would be:

    4(3/2)^(n - 1)

    but wait! what about the changing sign? do we just add (-1)^(n-1) as you suggested? well we could, or we could just change the common ratio to a negative. so

    a_n = 4(-3/2)^(n-1)

    try the same analysis for part c, see what you come up with. and what type of sequence is a?
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