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sweetcupcake

  • 3 years ago

the first term of a geometric series is -1, and the common ratio is -3. How many terms are in the series if its sum is 182?

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  1. sumanth4phy
    • 3 years ago
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    -1 +3 -9 +27......+-3^(n-2) + 3^(n-1) 3(1+9+27....3^(n-2)) -1(1+3+9+...3^(n-2)) =2(1+9+27+...3^(n-2)) = 182 => 1+9+....9^[(n-2)/2] = 91 =>( 9^(n/2) -1)/(9-1) = 91 =>3^n - 1 =728 =>3^n = 729 =>n=6

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