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Lilmike234

  • one year ago

The second term in a geometric sequence is 20. The fourth term in the same sequence is 45/4 or 11.25. What is the common ratio in this sequence?

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  1. campbell_st
    • one year ago
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    well a term in a geometric sequence is found using \[a_{n} = a \times r^{n -1}\] and you know the 2nd term \[20 = a \times r^{2 -1} ~~~or~~~20 = a \times r\] and he 4th term \[\frac{45}{4} = a \times r^3\] which can be written as \[\frac{45}{4} = a \times r \times r^2\] make the substitution for the 2nd term \[\frac{45}{4} = 20 \times r^2\] now you can solve for r

  2. campbell_st
    • one year ago
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    and there are 2 possible answerz for r

  3. lilmike234
    • one year ago
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    Which are 1/7 and 3 right ?

  4. campbell_st
    • one year ago
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    |dw:1437106434841:dw| so then simplify the fraction |dw:1437106495856:dw|

  5. campbell_st
    • one year ago
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    so take thhe square root of both sides... of the equation and you'll get the 2 answers

  6. lilmike234
    • one year ago
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    3/4 and 1/4 ?

  7. campbell_st
    • one year ago
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    well you are halfway correct |dw:1437107382618:dw|

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