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.

The first term of the progression is 15

Let the first 3 terms of the geometric progression be a/r, a, and ar

If the product of the first three terms of a geometric progression is 3375, then;

Hene the first term of the progression is 15

Learn more here: link

  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.

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.