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alisha [4.7K]
3 years ago
7

Find Four Numbers that form a geometric progression such that the second term is less than the first by 35, and the third term i

s greater than the fourth term by 560. (Note: there should be 3 different possible geometric sequences)
Mathematics
1 answer:
Olegator [25]3 years ago
8 0

Answer:

  • -35/3, -140/3, - 560/3, -2240/3
  • 7, -28, 112, - 448  

Step-by-step explanation:

<u>The terms are:</u>

  • a₁, a₂, a₃, a₄

<u>Given:</u>

  • a₁ = a₂ + 35
  • a₃ = a₄ + 560

<u>Use the nth term formula:</u>

  • a₂ = a₁r
  • a₃ = a₁r²
  • a₄ = a₁r³

<u>Substitute:</u>

  • a₁ = a₁r + 35 ⇒ a₁(1 - r) = 35
  • a₁r² = a₁r³ + 560  ⇒ a₁(1 - r)r² = 560

<u>Divide the second equation by the first:</u>

  • r² = 560/35
  • r² = 16
  • r = √16
  • r = ± 4

<u>Use the first equation to find the first term:</u>

  • a₁( 1 ± 4) = 35
  • 1. a₁ = 35/-3 = -35/3
  • 2. a₁ = 35/5 = 7

<u>We have two sequences:</u>

r = 4

  • -35/3, -140/3, - 560/3, -2240/3

r = -4

  • 7, -28, 112, - 448  
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