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blagie [28]
3 years ago
13

What is the answer to this pattern 12,24,72,288,______?

Mathematics
2 answers:
Arlecino [84]3 years ago
5 0
Answer and workings in the attachment below.

AveGali [126]3 years ago
3 0
If you notice, the pattern is multiplication.

12*2 = 24, 24*3 = 72, 72* 4 = 288, 288* x = y

Notice that it goes two-fold, then three-fold, then four-fold.  The next number would be 288*5, which is 1440.

Therefore, the next number is 1440.
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1)a_{n}=a_{1}+(n-1)d\Rightarrow a_{n}=-1-2(n-1)\\a_{2}=-1-2(2-1)\Rightarrow a_{2}=-3\\a_{3}=-1-2(3-1)\Rightarrow a_{3}=-5\\(...)\\a_{10}=-1-2(10-1)=-19

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Step-by-step explanation:

1) To write an Arithmetic Sequence, as an Explicit Term, is to write a general formula to find any term for this sequence following this pattern:

a_{n}=a_{1}+d(n-1)\Rightarrow \left\{\begin{matrix}a_{n}=n^{th}\: term\\a_1=1st \: term \\d=\: difference\\n=n^{th}\, term\end{matrix}\right.

<em>"Write an explicit formula for each explicit formula A(n)=-1+(n-1)(-2)"</em>

This isn't quite clear. So, assuming you meant

Write an explicit formula for each term of this sequence A(n)=-1+(n-1)(-2)

As this A(n)=-1+(n-1)(-2)  is already an Explicit Formula, since it is given the first term a_{1}=-1 the common difference d=-2 let's find some terms of this Sequence through this Explicit Formula:

a_{n}=a_{1}+(n-1)d\Rightarrow a_{n}=-1-2(n-1)\\a_{2}=-1-2(2-1)\Rightarrow a_{2}=-3\\a_{3}=-1-2(3-1)\Rightarrow a_{3}=-5\\(...)\\a_{10}=-1-2(10-1)=-19

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Then, just plug in the first term and the common difference into the explicit formula:

a_{10}=4+8(10-1)\Rightarrow a_{10}=76

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