MHB Determining if a sequence is arithmetic

[fluffertoes]

Question:

Find the first 5 terms of this series and determine if it is an arithmetic sequence.

A_n= 2 + 6n

Help please!

 

[MarkFL]

Re: Sequences and series help ASAP please!

Question:

Find the first 5 terms of this series and determine if it is an arithmetic sequence.

A_n= 2 + 6n

Help please!

If we have an AP, then we must have:

$$a_{n+1}-a_{n}=C$$ where C is some constant...is this what we have?

 

[fluffertoes]

Re: Sequences and series help ASAP please!

If we have an AP, then we must have:

$$a_{n+1}-a_{n}=C$$ where C is some constant...is this what we have?

All the info i was given is what I put in the original question up there, yikes

 

[MarkFL]

Re: Sequences and series help ASAP please!

All the info i was given is what I put in the original question up there, yikes

We are given:

$$a_{n}=2+6n$$

Therefore:

$$a_{n+1}=2+6(n+1)$$

So, what is the difference:

$$a_{n+1}-a_{n}$$ ?

 

[fluffertoes]

Re: Sequences and series help ASAP please!

We are given:

$$a_{n}=2+6n$$

Therefore:

$$a_{n+1}=2+6(n+1)$$

So, what is the difference:

$$a_{n+1}-a_{n}$$ ?

1? I'm not sure

 

[MarkFL]

Re: Sequences and series help ASAP please!

1? I'm not sure

Let's work it out...

$$a_{n+1}-a_{n}=\left(2+6(n+1)\right)-\left(2+6n\right)=\left(2+6n+6)\right)-\left(2+6n\right)=(2+6n)+6-(2+6n)=6$$

This tells us that any two successive terms in the given sequence differ by 6, which is a constant, and therefore we do have an arithmetic sequence. :)