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# Find the geometric mean of 5/8 and 5/18.?

Find the geometric mean of 5/8 and 5/18.

Find the sum S23 for the geometric series: -6 + 12 - 24 + 48...

Find the first three terms of the geometric sequence with a5 = -128 and a10 = 4096

### 3 Answers

- Φ² = Φ+1Lv 79 years agoFavorite Answer
GM = 5/8 * 5/18 = √(25/144) = 5/12

S23 = -16777218

(a1, a2, a3) = (-8,16,-32)

- fastLv 44 years ago
The geometric propose of two numbers, x and y, is given by geometric propose = sqrt(x*y) The mathematics propose of two numbers, x and y, is given by (x+y)/2 We also comprehend that x+5=y So (x+x+5)/2 - a million/2 = sqrt(x*(x+5)) x + 2.5 - 0.5 = sqrt(x^2 + 5x) x + 2 = sqrt(x^2 + 5x) x^2 + 4x + 4 = x^2 +5x 4 = x considering that y = x+5, y = 9 So both numbers are 4 and 9. The mathematics propose of four and 9 is (4+9)/2 = 6.5 (4+2.5 = 6.5 and six.5+2.5 = 9) The sensible geometric propose of four and 9 is sqrt(4*9) = sqrt(36) = 6 (4 * a million.5 = 6 and six * a million.5 = 9) because the maths propose of 6.5 is a million/2 more beneficial than the geometric propose of 6, this shows that we do certainly have the stunning solutions. i wish this facilitates!

- Mike GLv 79 years ago
sqrt(25/(8*18) = 5/12

a= -6 and r = -2 and n=23

S = -6(1-(-2)^23))/3 = -16,777,218

ar^4 = -128

ar^9 = 4096

r^5 = 4096/-128 = -32

r = -2

a = -128/16 = -8

First 3 terms

-8, 16, -32