MHB Determining if a sequence is arithmetic

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SUMMARY

The sequence defined by the formula An = 2 + 6n is confirmed to be an arithmetic sequence. The difference between successive terms, calculated as a_{n+1} - a_{n}, equals 6, which is a constant. The first five terms of the sequence are 2, 8, 14, 20, and 26. This demonstrates that the sequence adheres to the definition of an arithmetic progression (AP).

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fluffertoes
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Question:

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

An= 2 + 6n

Help please!
 
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Re: Sequences and series help ASAP please!

fluffertoes said:
Question:

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

An= 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?
 
Re: Sequences and series help ASAP please!

MarkFL said:
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
 
Re: Sequences and series help ASAP please!

fluffertoes said:
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:

$$a_{n+1}-a_{n}$$ ?
 
Re: Sequences and series help ASAP please!

MarkFL said:
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
 
Re: Sequences and series help ASAP please!

fluffertoes said:
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. :)
 

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