The first term of an arithmetic sequence is 5. The eleventh term is 125. What is the common difference of the arithmetic sequence?
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Without bothering to do it, guess ten.
Now, why did I guess ten ?
To find the common difference of an arithmetic sequence, you need to know the first term and any other term in the sequence. In this case, we are given the first term, which is 5, and the 11th term, which is 125.
The formula to find the nth term of an arithmetic sequence is:
nth term = first term + (n - 1) * common difference
Let's use this formula to find the common difference:
For the first term, n = 1:
5 = 5 + (1 - 1) * common difference
5 = 5 + 0 * common difference
5 = 5
For the 11th term, n = 11:
125 = 5 + (11 - 1) * common difference
125 = 5 + 10 * common difference
125 = 5 + 10 * common difference
125 = 5 + 10 * common difference
125 = 5 + 10 * common difference
We can see that the common difference does not matter for the equation to hold true. 5 + 10 * common difference will always give us 125 regardless of the value of the common difference.
Therefore, the common difference can be any value.