Question

Find the explicit formula for the arithmetic sequence cn given below. Note that c1=8. 8,17,26,35,44,…

Answer 1

`c_n=9\,n-1`

Explanation:

Recall that the general formula for the nth term of an arithmetic sequence is given by:

`c_n=c_1+(n-1)\,d`

where
`c_1` is the first term of the sequence (in our case 8), and
`d` is the common difference for the sequence (the number that is added to a term in order to get the term that follows. In our case, "9" is the common difference (you can check this by subtraction between any two consecutive terms.

Then, the formula for the nth term of this sequence is

`c_n=8+(n-1)\,9=8+9\,n-9=9\,n-1`