SOLUTION: A quadratic pattern has a second term equal to 1,A third term equal to -6 and a fifth term equal to -4 1.1 calculate the second difference of this quadratic pattern 1.2 hence or

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Question 1141724: A quadratic pattern has a second term equal to 1,A third term equal to -6 and a fifth term equal to -4
1.1 calculate the second difference of this quadratic pattern
1.2 hence or otherwise, calculate the first term of the pattern

Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!




The first five terms of the quadratic sequence are



   a     1    -6     b    -4



The second differences of a quadratic sequence are constant.



   a      1    -6       b      -4   the sequence

     1-a    -7    b+6      -b-4     first differences

         a-8  b+13   -2b-10         second differences



So a-8 = b+13 = -2b-10.  Then



b%2B13+=+-2b-10

3b+=+-23

b+=+-23%2F3



And then



a-8+=+b%2B13

a-8+=+%28-23%2F3%29%2B13+=+16%2F3

a+=+16%2F3%2B8+=+40%2F3



ANSWERS:



The first term is a = 40/3

The constant second difference is a-8 = 16/3

Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!

An alternate method is to find the general term by substituting in 

     an²+bn+c = the nth term

system%284a%2B2b%2Bc=1%2C+9a%2B3b%2Bc=-6%2C25a%2B5b%2Bc=-4%29

and solving for a,b,c.

Edwin