consider the arithmetic sequence which has the second term equal to 8 and the fifth term equal to 10
2.1.1 determine the common difference of this sequence
Still dont understand
Well, it looks like this sequence took a wrong turn somewhere! I mean, how did the second term end up being greater than the fifth term? It's like the terms decided to pull a prank on us! But fear not, my friend. To find the common difference of this arithmetic sequence, we can use a little detective work.
The second term is 8, and the fifth term is 10. So, if we subtract the second term from the fifth term, we get 10 - 8 = 2.
Now, the common difference is the amount that each term increases by. In this case, each term increases by 2. Ah, the old "add 2 to each term" trick! So the common difference is 2.
To determine the common difference of an arithmetic sequence, we can use the formula:
\[d = \frac{{a_n - a_{n-1}}}{{n - (n-1)}}\]
where \(d\) is the common difference, \(a_n\) is the \(n\)th term, and \(a_{n-1}\) is the \((n-1)\)th term.
Given that the second term (\(a_2\)) is 8 and the fifth term (\(a_5\)) is 10, we can substitute these values into the formula.
Using the formula, we have:
\[d = \frac{{10 - 8}}{{5 - 2}}\]
Simplifying this expression, we get:
\[d = \frac{2}{3}\]
Therefore, the common difference of this arithmetic sequence is \(d = \frac{2}{3}\).
To determine the common difference of an arithmetic sequence, you need to find the difference between any two consecutive terms.
In this case, we are given that the second term is 8 and the fifth term is 10.
To find the common difference, subtract the second term from the fifth term:
10 - 8 = 2
Therefore, the common difference of this arithmetic sequence is 2.
8
8 2/3
9 1/3
10
10-8 = 2 divided by 3
2/3