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anonymous

  • one year ago

Given the geometric sequence 3, 6, 12, 24, …, what is a1, the first term? What is r, the common ratio? Find the 8th term of this sequence. What formula did you use? Be sure to show your work.

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  1. johnweldon1993
    • one year ago
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    \(\large a_1 = 3\) this is the first number in your sequence r, hint* What number do you need to multiply to each previous number to get to the next?

  2. anonymous
    • one year ago
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    can you explain more

  3. johnweldon1993
    • one year ago
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    Alright, so that a1 was pretty self explanatory so I'm assuming you have that! lol So the 'r' the common ratio We multiply each number by this 'r' to get to the following number Here the sequence is 3,6,12,24 right? To get from 3 to 6...what number do we multiply by?

  4. anonymous
    • one year ago
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    2

  5. johnweldon1993
    • one year ago
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    Right, so our common ratio is 2 Just to check it is consistent To get from 6 to 12 we also multiply by 2 and to get from 12 to 24 we again multiply by 2 Okay so good, we have our a1 and our 'r' Now we need to find the 8th term right?

  6. anonymous
    • one year ago
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    yep

  7. johnweldon1993
    • one year ago
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    Alright, so then to find any term of a geometric sequence, we use the formula \[\large a_n = a_1 \times r^{n-1}\] So here, since we want the 8th term...we simply plug in 8 for 'n'...still 2 for 'r' and still 3 for 'a1' so we have \[\large a_8 = 3\times 2^{8-1}\] \[\large a_8 = 3\times 2^{7} = ?\]

  8. anonymous
    • one year ago
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    384

  9. johnweldon1993
    • one year ago
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    And that is correct!

  10. anonymous
    • one year ago
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    thats it?

  11. anonymous
    • one year ago
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    thanks

  12. johnweldon1993
    • one year ago
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    Yeah that is it! No problem!

  13. anonymous
    • one year ago
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    can you help me with another problem?

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