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Galina-37 [17]
3 years ago
11

Please help lots of points rewarded

Mathematics
2 answers:
castortr0y [4]3 years ago
8 0

Answer:

  • tₙ =  2n² - 3

Step-by-step explanation:

<u>Standard form of a quadratic equation:</u>

  • y = ax² + bx + c

<u>Apply same for the quadratic sequence:</u>

  • tₙ = an² + bn + c

<u>Substitute n with 1, 2 and 3 to get the system:</u>

  • -1 = a*1² + b*1 + c  ⇒ a + b + c = -1
  • 5 = a*2² + b*2 + c  ⇒ 4a + 2b + c = 5
  • 5 = a*3² + b*3 + c  ⇒ 9a + 3b + c = 15

<u>Subtract the first equation from the second and subtract the second equation from the third to get:</u>

  • 3a + b = 6
  • 5a + b = 10

<u>Again subtract the equations to find a:</u>

  • 2a = 4
  • a = 2

<u>Then find b and c:</u>

  • b = 3a - 6 = 6 - 6 = 0
  • c = -1 - a - b = -1 - 2 - 0 = -3

<u>Substitute the coefficients back into the equation of the quadratic sequence:</u>

  • tₙ = 2n² + 0n + (-3) = 2n² - 3
ololo11 [35]3 years ago
6 0
A of n = 2n^2 - 3
the nth term = 2 times n to the power of 2 minus 3
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