The first three terms of an arithmetic sequence are 2k+1, 5k, 7k+2. What is the value of k?

Step-by-step explanation:

In an arithmetic sequence, we keep adding/subtracting to get the next term in the sequence.

Therefore, we can make an equation that looks like this:

5k-(2k+1) = 7k+2-5k

We can subtract 2k+1 from 5k, and 5k from 7k+2, because from subtracting the difference would be the same. (common difference of sequence is what we would find)

Now, we just need to simplify.

5k-2k-1 = 2k+2

3k-1=2k+2

Now let's combine like terms, and we get:

k=3

Hope this helped!

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Explanation: