fluffertoes said:Question:
Find the first 5 terms of this series and determine if it is an arithmetic sequence.
An= 2 + 6n
Help please!
MarkFL said:If we have an AP, then we must have:
\(\displaystyle a_{n+1}-a_{n}=C\) where C is some constant...is this what we have?
fluffertoes said:All the info i was given is what I put in the original question up there, yikes
MarkFL said:We are given:
\(\displaystyle a_{n}=2+6n\)
Therefore:
\(\displaystyle a_{n+1}=2+6(n+1)\)
So, what is the difference:
\(\displaystyle a_{n+1}-a_{n}\) ?
fluffertoes said:1? I'm not sure
To determine if a sequence is arithmetic, you need to check if there is a constant difference between each consecutive term. If there is a consistent difference, the sequence is arithmetic.
The formula for an arithmetic sequence is an = a1 + (n-1)d, where an represents the nth term, a1 is the first term, and d is the common difference.
Yes, an arithmetic sequence can have a negative common difference. This means that the terms in the sequence are decreasing in value.
An arithmetic sequence has a constant difference between each consecutive term, while a geometric sequence has a constant ratio between each consecutive term. In an arithmetic sequence, the difference between terms stays the same, whereas in a geometric sequence, the terms are multiplied by a constant factor.
The arithmetic mean of a sequence is the average of all the terms in the sequence. If the arithmetic mean is equal to the first term in the sequence, then the sequence is arithmetic. If the arithmetic mean is not equal to the first term, then the sequence is not arithmetic.