Question

Sum of three consecutive numbers in GP is 42 and their product is 512 find the number

Answer 1

Heya user,

let the three terms be a/r, a, ar ... with ratio = r;

Then (a/r) * a * ar = 512
=>a³ = 512
=>a = 8 or -8

Now, a/r + a + ar = 42
=> 1/r + 1 + r = 5.25
=> 1/r + r = 4.25
=> r² - 4.25r + 1 = 0
=> 2r = 4.25 + 3.75 or 4.25 - 3.75
=> 2r = 8 or 0.5
=> r = 4 or 0.25

Also, if a=-8;
a/r + a + r = 42
=> 1/r + 1 + r = -5.25
=> 1/r + r = -6.25
=> r² + 6.25r + 1 = 0
=> 2r ≈ -6.25 + 5.9  or -6.25 - 5.9
=> r ≈ -0.48 or -6.75

Here, we'll neglect the negative values to get the req.d terms as:

a = 8, r = 4 ===> 2,8,32
or a=8, r = 0.25 ===> 32,8,2