Question

The product of three terms of a gp is 512. If 8 is added to the first term and 6 to the second term, find the new terms forms of an ap

Answer 1

Answer:

(x + 8) + (x + 6) + x = 512

3x + 14 - 14 =512 - 14

3x = 498

x = 498/3 = 166

Therefor (166 + 8) + (166 + 6) + 166 = 512

174 + 172 + 166 = 512

Step-by-step explanation:

Answer 2

Let the 3 number in the geometric sequence be a/r, a and ar.

The product of the three numbers is a^3 = 512, So a = 8.

Now (a/r) +8, a+6, ar form an AP.

So we have: ar - (a+6) = a+6 - (a/r)-8, or

ar^2-ar-6r = ar+6r-a-8r, or

8r^2–8r-6r = 8r+6r-8–8r, or

8r^2–14r-6r +8 = 0

8r^2–20r+8 = 0, or

2r^2–5r +2= 0, or

(2r-1)(r-2) = 0

Hence r =2 or 1/2.

So the three terms of the GP are 4, 8 and 16 or 16, 8 and 4.

Check: 4+8, 8+6, 16 = 12, 14 16, all in AP.