Question

what is the nth term of the sequence -2 -8 -18 -32 -50

Answer 1

Answer:

-2n²

Step-by-step explanation:

Using the image attached:
We see that the second differences (blue ones) are all equal so we conclude that this is a quadratic sequence.
The quadratic sequence has the form:
$T_{n} = an^{2} +bn +c$

To find the value of a we just divide second difference ( -4 ) by 2:

• $a = \frac{-4}{2}= -2$

Now we have:

• $T_{n}= -2n^{2} +bn+c$

Substitute $n_{1}$ and $n_{2}$ into the equation above:

• $T_{1} = -2(1)^{2} +b(1) +c$

• $T_{2} = -2(2)^{2} +b(2)+c$

Since $T_{1}$ = -2 and $T_{2}$ = -8 , after simplification we have:

• $b +c =0$
• $2b+c=0$

The solution of this system is:

• b=0, c =0

The general term is :

$T_{n} = -2n^{2}$