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