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

In summary, the first four terms of the sequence defined by the recursion $a_{n+1}=a_n+n$, $a_1=-1$ are -1, 0, 2, 5.
  • #1
karush
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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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  • #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.

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

\(\displaystyle a_{1+1}=a_2=a_1+1=-1+1=0\)

Can you proceed?
 
  • #3
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:

\(\displaystyle a_{1+1}=a_2=a_1+1=-1+1=0\)

Can you proceed?
\(\displaystyle a_{2+1}=a_3=a_1+1=-1+2=1\)
\(\displaystyle a_{3+1}=a_4=a_1+1=-1+3=2\)
$\textsf{so the first 4 terms are } $ $-1,0,1,2$
 
  • #4
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:
\(\displaystyle a_{2+1}=a_3=a_1+1=-1+2=1\)
\(\displaystyle a_{3+1}=a_4=a_1+1=-1+3=2\)
$\textsf{so the first 4 terms are } $ $-1,0,1,2$

We have:

\(\displaystyle a_1=-1\)

\(\displaystyle a_{1+1}=a_2=a_1+1=-1+1=0\)

\(\displaystyle a_{2+1}=a_3=a_2+2=0+2=2\)

\(\displaystyle a_{3+1}=a_4=a_3+3=2+3=5\)
 
  • #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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  • #6
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:

\(\displaystyle a_{n+1}=a_{n}+n\)

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
 

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

What is the first term in the sequence?

The first term in the sequence is -1.

What is the second term in the sequence?

The second term in the sequence is 0. (calculated by plugging in n=1 into the formula)

What is the third term in the sequence?

The third term in the sequence is 2. (calculated by plugging in n=2 into the formula)

What is the fourth term in the sequence?

The fourth term in the sequence is 5. (calculated by plugging in n=3 into the formula)

What is the general formula for finding the nth term in the sequence?

The general formula for finding the nth term in the sequence is π‘Ž_𝑛=𝑛(𝑛+1)/2 - 1.

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