Question

here are the first five terms of a quadratic sequence (1 8, 21, 40, 65). the nth term of this sequence can be written in the form (an2 + bn). where a and b are integers. work out the value of a and the value of b

Answer 1

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

=$an^2+bn$

We have to find the value of a and b where a and b are integers.

For n=1

$a+b=1$   ......(1)

For n=2

$(2)^2a+2b=8$

$4a+2b=8$

$2a+b=4$   .....(2)

Subtract equation (1) from (2) we get

$2a-a=4-1=3$

$a=3$

Using the value of a=3 in equation (1)

$3+b=1$

$b=1-3=-2$

Hence, the value of

a=3 and b=-2