Question

HELP FAST PLEASE 10 POINTS

Answer 1

The nth term of the quadratic sequence is
`n^2+2n`.

Explanation:

Since the given sequence is a quadratic sequence.

Let the terms be of the form
`an^2+bn+c`.

So, we have,

At n= 1,
`a+b+c=3` .......................(1)

At n= 2,
`4a+2b+c=8` .......................(2)

At n=3,
`9a+3b+c=15` .......................(3)

By (1) and (2), we have,

`3-a-b=8-4a-2b` i.e.
`3a+b=5` ...............(4)

By (1) and (3), we have,

`3-a-b=15-9a-3b` i.e.
`8a+2b=12` i.e.
`4a+b=6` ........(5)

Subtracting (4) and (5), we get,
`a=1`

So, (4) implies
`3* 1+b=5` i.e.
`b= 5-3` i.e.
`b= 2`

So, from equation (1), we get,

`a+b+c=3` i.e.
`1+2+c=3` i.e.
`3+c=3` i.e.
`c=0`

Hence, the terms of the given sequence are of the form,
`n^2+2n`

That is, the nth term of the quadratic sequence is
`n^2+2n`.