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The first two terms of a quadratic sequence are 10 and 17
Here is some information about the sequence.
1st
2nd
term
term
Sequence
First
difference
10
+7
17
+13
+6
3rd
term
*******
Second
difference
Work out an expression for the nth term of the sequence.
+6
4th
term
*******

The first two terms of a quadratic sequence are 10 and 17 Here is some information about the sequence 1st 2nd term term Sequence First difference 10 7 17 13 6 3 class=

Respuesta :

Answer:

  • 3n^2-2n+9

Step-by-step explanation:

  • The general term for a quadratic pattern is an^2+bn+c
  • a = half the second difference
  • a = 3
  • So now we have 3n^2+b+c
  • t(1)=10
  • 3(1)^2+(1)b+c
  • 3+b+c=10
  • b+c=7
  • t(2)=17
  • 3(2)^2+b(2)+c=17
  • 12+2b+c=17
  • 2b+c=5
  • now we solve the simultaneous equations
  • 2b+c=5
  • b+c=7
  • we make the c cancel out
  • 2b+c=5
  • -b-c=-7
  • b= -2
  • now we solve for c by substituting b back into the equation
  • 2b+c=5
  • 2(-2)+c=5
  • -4+c=5
  • c=9
  • we can verify the solutions as follows
  • b+c=7
  • -2 +9 = 7
  • 7=7
  • Hence, the nth term is 3n^2-2n+9

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