MHB -z78 first four terms of the sequence of 𝑎_(𝑛+1)=𝑎_𝑛+𝑛,𝑎_1=−1.

[karush]

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

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

$\text{stuck!}$

 

[MarkFL]

Re: Write out the first four terms of the sequence defined by the recursion 𝑎_(𝑛+1)=𝑎_𝑛+𝑛,𝑎_1=−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?

 

[karush]

Re: Write out the first four terms of the sequence defined by the recursion 𝑎_(𝑛+1)=𝑎_𝑛+𝑛,𝑎_1=−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?

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

 

[MarkFL]

Re: Write out the first four terms of the sequence defined by the recursion 𝑎_(𝑛+1)=𝑎_𝑛+𝑛,𝑎_1=−1.

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

We have:

$$a_1=-1$$

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

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

$$a_{3+1}=a_4=a_3+3=2+3=5$$

 

[karush]

Re: Write out the first four terms of the sequence defined by the recursion

so $a_1$ is not a constant but is replaced

 

[MarkFL]

Re: Write out the first four terms of the sequence defined by the recursion 𝑎_(𝑛+1)=𝑎_𝑛+𝑛,𝑎_1=−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