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Answer:

[tex] \pmb{SOLUTION:-}[/tex]

  • 5,x,125 are in continued proportion,

Then,

[tex] \displaystyle{ \frac{5}{x} = \frac{x}{125} }[/tex]

[tex]5 \times 125 = {x}^{2} [/tex]

[tex] {x}^{2} = 625[/tex]

[tex]x = \sqrt{625} [/tex]

[tex]x = 25[/tex]

Answer:

  • a₂ = ±25

Step-by-step explanation:

  • 5, x, and 125 are part of a geometric progression

What we know :

  • a (first term) = 5
  • aₙ (final term) = 125
  • n (number of terms) = 3

Finding the common ratio (r)

  • aₙ = arⁿ⁻¹
  • 125 = (5)(r)³⁻¹
  • 25 = r²
  • r = ± 5

Finding x

  • x is the 2nd term of the progression
  • a₂ = ar
  • a₂ = 5(±5)
  • a₂ = ±25

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