Question

Find the 82nd term of the arithmetic sequence -8, 9, 26, ...

Answer 1

The 82nd term would be 1,369.
First we need to find an equation to represent this sequence, which we can do by finding the common difference between terms and then comparing those multiples to the sequence.
To find the common difference we simply need to do 9 - -8 = 17, and this is the same as 26 - 9 = 17, so we know that it will be the same for the whole sequence.
Then we can write multiples of 17 above the original sequence and find the difference:
17, 34, 51
-8, 9, 26
The difference between 17 and -8 is -25, so our final equation becomes:
17n - 25
Then we just substitute in 82 as n because we’re looking for the 82nd term and we get 17(82) - 25 = 1394 - 25 = 1369
I hope this helps!