math

1. Examine the first four terms in each of the following number sequences:
*2, 7, 12, 17 my formula x+5
*7, 21, 63, 189, 567 my formula x(2)+x
*1000, 850, 700, 550 my formula x-150
* –10, –6, –2, 2 my formula x+4

For each sequence, what would be the 20th and 100th term? Explain your reasoning for each.

For which of the sequences would the number 352 be a term? Explain your reasoning.

One of the sequences is different from the other three. Describe what makes the one different and the other three "alike."

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  1. All your choices are correct except the 2nd

    look at the terms:
    7, 21, 63, 189, 567, ...
    or
    7*1, 7*3, 7*9, 7*27, 7*81

    looks like 7* 3^(x-1)

    btw, that sequence is the one that different from all the others, because it is NOT an arithmetic sequence.

    For the 20th and 100th term, I will do the first, you repeat the same method for the others

    for 2 7 12 17 ...
    a = 2, d = 5
    term 20 = a + 19d
    = 2 + 19(5) = 97

    term 100 = a + 99d
    = 2 + 99(5) = 497

    As to 352 being one of the terms?

    let the term number be n
    term n = a + (n-1)d
    2 + (n-1)(5) = 352
    5n - 5 = 350
    5n = 355
    n = 71

    yes, 352 is the 71st term in the first sequence
    repeat for the 3rd and 4th sequence

    testing for the 2nd sequence
    7*(3)^(n-1) = 352
    3^(n-1) = 352/7
    which clearly is NOT a power of 3, so 352 does not belong to the 2nd sequence

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  2. 7*1, 7*3, 7*9, 7*27, 7*81

    looks like 7* 3^(x-1) I don't understand how you got (x-1) can you explain?

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  3. The multipliers are

    1,3,9,27, ...
    As powers of 3, those are 0,1,2,3,...

    You can't say 7*3^x because the first term (x=1) has not been multiplied yet.

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