SOLUTION: A quadratic pattern has a second term equal to 1 a third term equal to -6 and a fifth term equal to -14 1.1 Calculate the second difference of this quadratic pattern 1.2 Hence o

Question 1190438: A quadratic pattern has a second term equal to 1 a third term equal to -6 and a fifth term equal to -14
1.1 Calculate the second difference of this quadratic pattern
1.2 Hence or otherwise calculate the first term of the pattern
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

   ___   1     -6       x        -14     the given 2nd, 3rd, and 5th terms, and the unknown 4th term
      ___   -7    x+6      -14-x         the first differences
         ___  x+13   -2x-20              the second differences

In a quadratic sequence, the second differences are constant

x+13=-2x-20
3x=-33
x=-11

Rewrite the array using x=-11; and show the constant second difference

   ___   1     -6      -11        -14
      ___   -7     -5        -3
          2     2       2

Work back up the array to find the first term of the sequence

    10   1     -6      -11        -14
       -9    -7     -5        -3
          2     2       2

ANSWERS:
1.1 The constant second difference is 2
1.2 The first term is 10

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