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anonymous

  • one year ago

The 1st term of an arithmetic progression is a and the common difference is d, where d does not equal 0. (i) Write down expressions, in terms of a and d, for the 5th term and the 15th term. The 1st term, the 5th term and the 15th term of the arithmetic progression are the first three terms of a geometric progression. (ii) Show that 3a=8d I need help with (ii) please! I have the equations for (i) they are a + 4d ; a +14d

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  1. DanJS
    • one year ago
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    have you done anything yet?

  2. anonymous
    • one year ago
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    I actually don't even know where to start so no.

  3. DanJS
    • one year ago
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    first, you have to figure what an arithmetic progression is

  4. anonymous
    • one year ago
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    well I know what that is already

  5. DanJS
    • one year ago
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    Arithmetic sequence of numbers ---starts at a, and each consecutive term is 'd' away from the last term

  6. DanJS
    • one year ago
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    a general form for the nth term is, \[a _{n} = a _{1} + (n - 1)*d\]

  7. anonymous
    • one year ago
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    yes, i have the answers for the first question already figured out, its the second one i would like help with please

  8. DanJS
    • one year ago
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    the nth term = the first term + (n-1) d

  9. anonymous
    • one year ago
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    ok

  10. DanJS
    • one year ago
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    do you know what a geometric series is?

  11. DanJS
    • one year ago
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    instead of an linear change from term to term, geometric series multiplies each by a common ratio r, every term / the one before it = r , and it is constant

  12. DanJS
    • one year ago
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    The three terms from the last series to use are a ; a + 4d ; a + 14d

  13. anonymous
    • one year ago
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    Yes

  14. DanJS
    • one year ago
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    the common ratio between terms is r = (a + 4d) / a and r = (a + 14d)/(a+4d)

  15. DanJS
    • one year ago
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    general geometric series to get the nth term Nth Term = (FIrst Term) * r^n

  16. DanJS
    • one year ago
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    exponential

  17. DanJS
    • one year ago
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    really all you have to do is know that the ratio of consecutive terms is always the same value r

  18. DanJS
    • one year ago
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    set those two ratios equal, and solve for 3a to show it equals 8d

  19. DanJS
    • one year ago
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    \[\frac{ a+4d }{ a } = \frac{ a+14d }{ a+4d }\] = r

  20. DanJS
    • one year ago
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    solve for 3a = ... should come to that 8d value

  21. anonymous
    • one year ago
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    Ok when you say solve for 3a how would I do that exactly (sorry)

  22. DanJS
    • one year ago
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    just start moving things around and expanding and isolating a to one side and d to the other side

  23. DanJS
    • one year ago
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    cross multiply first, for example

  24. DanJS
    • one year ago
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    (a+4d)*(a+4d) = a*(a+14d)

  25. DanJS
    • one year ago
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    expand all those out from disributing

  26. DanJS
    • one year ago
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    should be left with what they are looking for

  27. anonymous
    • one year ago
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    Ok, will try that quickly

  28. anonymous
    • one year ago
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    Hooray I got the right answer! Thank you very much for your help!

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