Question

The product of the first three terms of a geometric progression is 3375, and their sum is 65. Find the first term of this progression.

Answer 1

Answer:

  5 or 45

Step-by-step explanation:

If the first term is "a" and the common ratio is "r", then the first three terms are ...

  a, ar, ar²

Their product will be ...

  a × ar × ar² = (ar)³ = 3375

  ar = ∛3375 = 15

Their sum will be ...

  a + ar + ar² = 65 = 15/r + 15 + 15r

Subtracting 15 and multiplying by r/5, we have the quadratic in r:

  10r = 3 + 3r²

  3r² -10r +3 = 0 . . . . in standard form

  (3r -1)(r -3) = 0 . . . . factored

  r = 1/3 . . or . . 3 . . . . values of r that make the factors zero

The first term is 15/r = 45 or 5

_____

The first three terms could be 5, 15, 45; or they could be 45, 15, 5.