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Science & Mathematics by Anonymous 2018-05-12 21:09:20
Social Science
The 2nd and 8th terms of a geometric progression are -6 and -384. Find the sum of the 3rd and 7th term. Assume common ratio is positive.?
3 answers
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Anonymous
common ratio r > 0 a₂ = -6 a₈ = a₂r⁸⁻² = (-6)r⁶ = -384 r⁶ = 64 r = 64^(⅙) = 2 a₃ = a₂r = -12 a₇ = a₈/r = 192 a₃+a₇ = 180
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Anonymous
-6 = ar -384 = ar^7 r^6 = 64 r = 2 & a = -3 a_3 = -12 a_7 = -192 Answer -204
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Anonymous
r = ⁶√(-384/-6) = ⁶√64 = 2 (assuming a positive, real common ratio), so... -6r + -384/r = -6*2 - 384/2 = -12 - 192 = -204 is the sum of the 3rd and 7th term.
