Math (pre-calculus)

Hi! I have a question! I forgot how to do these two problems, and I need some help in solving them! Thanks so much!

1.) Find the first 5 terms of the sequence given by a1=2, an=3an-1 -1.

(It's: a sub 1 =2, a sub n= 3a sub n-1 -1)
Does that make sense?

If not, that's ok. I'll to clarify more if it's still strange (which it is, I know!)

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  1. asub1 = 2 is the first term

    asubn can be calculated fron asubn-1, using the formula you prodided
    asubn = 3 asubn-1 -1

    Thus a sub2 = 3 asub1 - 1 = 5
    asub3 = 3 asub2 -1 = 14
    asub4 = 3 asub3 -1 = 41
    asub5 = ?

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  2. Okay!! I think I got it!!! Thank you so much! I'm gonna solve the 5 terms, and write them up here! :) Tell me how I did!

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  3. Okay:

    a sub1=2
    a sub2= 3(2)-1=5
    a sub3= 3(5)-1=14
    a sub4= 3(14)-1=41
    a sub5= 3(41)-1=122

    I think that's it! Thanks so much again!

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  4. Looks good to me!

    It's interestng that the differences between adjacent terms are powers of 3:
    3,9,27,81 etc

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  5. The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 18 HCF of water is $33.44 , and the cost for using 35 HCF is $61.49. What is the cost for using 27 HCF of water?

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