2 years ago

Can you help me with these 2 questions?

Mathematics

1 answer:

Alenkinab [10]2 years ago

6 0

Answer:

What school you go to

Step-by-step explanation:

step by step go catch friend and step by step friends

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

andreev551 [17]

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-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:

$b +c =0$
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The solution of this system is:

b=0, c =0

The general term is :

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

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1 year ago