Find three consecutive terms of a geometric sequence such that their some is 35 and their product is 1000. Show all of the steps?

Answer 1

Let the three consecutive terms of the geometric sequence be a, ar, and ar^2. Then, we have:

a + ar + ar^2 = 35 (1) a * ar * ar^2 = 1000 (2)

From equation (2), we get:

a^3 * r^3 = 1000 ar = 10

Substituting ar = 10 in equation (1), we get:

a + 10 + 10r = 35 a + r = 25/2

Solving for a and r, we get:

a = 5/2 - sqrt(65)/2 r = 5/2 + sqrt(65)/2

Therefore, the three consecutive terms of the geometric sequence are:

a ≈ -7.37, ar ≈ -18.53, and ar^2 ≈ -46.34.

I hope this helps! Let me know if you have any other questions.