How do you find the explicit formula for the following sequence 10, 14, 18, 22, 24, ...?
Hi there! As mentioned in the comments below, I believe that the 24 should be a 26 to make this a nice sequence. If this is true, this is an arithmetic sequence with a common difference of 4.
The expression for the explicit formula of an arithmetic sequence is:
Looking at the sequence:
10, 14 18, 22, 26 we can deduce that:
And this is all you need, since you're finding an explicit formula (a formula that works for any n value).
Substituting this information into the general formula we get:
If you want, you can simplify this:
And that's it! That's the explicit formula! After determining the general formula for a sequence, it is always a good idea to double-check to see if it actually works with the numbers in your sequence. Lets do that:
We know, by extension, that the 6th term in the sequence should be 30 and therefore, if we sub 6 into "n" of our general formula we get:
We got what we were looking for! Thus, our explicit formula works! Hopefully this was all clear and straightforward! If you have any questions, please feel free to let me know! :)