Respuesta :

mhanifa

Answer:

  • The first car costs $40 and the price difference is $5

Step-by-step explanation:

Given:

  • There are 17 cars with the price as an AP sequence.
  • The total of 17 is $1360

The total of last 3 is $345, it means the total of the first 14 is:

  • $1360 - $345 = $1015

Use the sum of the first n terms formula, consider the first term is a and common difference is d:

  • Sₙ = (2a + (n - 1)d)*n/2

Find it at n = 14 and n = 17:

  • S₁₄ = (2a + 13d)*14/2 = 1015 ⇒ 2a + 13d = 1015/7  ⇒ 2a + 13d = 145
  • S₁₆ = (2a + 16d)*17/2 = 1360 ⇒ 2a + 16d = 2*1360/17 ⇒ 2a + 16d = 160

Subtract the equations and solve for d:

  • 16d - 13d = 160 - 145
  • 3d = 15
  • d = 5

Find the value of a:

  • 2a + 13*5 = 145
  • 2a + 65 = 145
  • 2a = 80
  • a = 40

Hi there.

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