MHB -z78 first four terms of the sequence of π‘Ž_(𝑛+1)=π‘Ž_𝑛+𝑛,π‘Ž_1=βˆ’1.

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Write out the first four terms of the sequence defined by the recursion n_(n+1)=n_1+1,n_1=βˆ’1

$\text{Write out the first four terms of the sequence defined by the recursion}$
$$\displaystyle
a_{n+1}=a_1+1,a_1=βˆ’1$$.
$\text{so then}$
$$\displaystyle
a_{0+1}=-1+0=-1$$

$\text{stuck!}$
 
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Re: Write out the first four terms of the sequence defined by the recursion π‘Ž_(𝑛+1)=π‘Ž_𝑛+𝑛,π‘Ž_1=βˆ’1.

We are given the first term, so we need to manually compute the next 3 terms...here's the second one:

$$a_{1+1}=a_2=a_1+1=-1+1=0$$

Can you proceed?
 
Re: Write out the first four terms of the sequence defined by the recursion π‘Ž_(𝑛+1)=π‘Ž_𝑛+𝑛,π‘Ž_1=βˆ’1.

MarkFL said:
We are given the first term, so we need to manually compute the next 3 terms...here's the second one:

$$a_{1+1}=a_2=a_1+1=-1+1=0$$

Can you proceed?
$$a_{2+1}=a_3=a_1+1=-1+2=1$$
$$a_{3+1}=a_4=a_1+1=-1+3=2$$
$\textsf{so the first 4 terms are } $ $-1,0,1,2$
 
Re: Write out the first four terms of the sequence defined by the recursion π‘Ž_(𝑛+1)=π‘Ž_𝑛+𝑛,π‘Ž_1=βˆ’1.

karush said:
$$a_{2+1}=a_3=a_1+1=-1+2=1$$
$$a_{3+1}=a_4=a_1+1=-1+3=2$$
$\textsf{so the first 4 terms are } $ $-1,0,1,2$

We have:

$$a_1=-1$$

$$a_{1+1}=a_2=a_1+1=-1+1=0$$

$$a_{2+1}=a_3=a_2+2=0+2=2$$

$$a_{3+1}=a_4=a_3+3=2+3=5$$
 
Re: Write out the first four terms of the sequence defined by the recursion

so $a_1$ is not a constant but is replaced
 
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Re: Write out the first four terms of the sequence defined by the recursion π‘Ž_(𝑛+1)=π‘Ž_𝑛+𝑛,π‘Ž_1=βˆ’1.

The recursive definition is:

$$a_{n+1}=a_{n}+n$$

So, when we compute $a_2$, we let $n=1$, and so only then will we have $a_1$ on the RHS of the definition. :D
 
Hi everybody If we have not any answers for critical points after first partial derivatives equal to zero, how can we continue to find local MAX, local MIN and Saddle point?. For example: Suppose we have below equations for first partial derivatives: βˆ‚Ζ’/βˆ‚x = y + 5 , βˆ‚Ζ’/βˆ‚y = 2z , βˆ‚Ζ’/βˆ‚z = y As you can see, for βˆ‡Ζ’= 0 , there are not any answers (undefined)

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