Answer:
a=3 and b=-2
Step-by-step explanation:
We are given that five terms of a quadratic sequence are
1 8, 21, 40, 65.
The nth term of this sequence
=[tex]an^2+bn[/tex]
We have to find the value of a and b where a and b are integers.
For n=1
[tex]a+b=1[/tex] ......(1)
For n=2
[tex](2)^2a+2b=8[/tex]
[tex]4a+2b=8[/tex]
[tex]2a+b=4[/tex] .....(2)
Subtract equation (1) from (2) we get
[tex]2a-a=4-1=3[/tex]
[tex]a=3[/tex]
Using the value of a=3 in equation (1)
[tex]3+b=1[/tex]
[tex]b=1-3=-2[/tex]
Hence, the value of
a=3 and b=-2
