a) How many terms are there in the arithmetic series
?
b) What is the sum of the series?

To find the number of terms in the arithmetic series , we first identify the first term and the common difference . The -th term of an arithmetic sequence is given by the formula . Setting the -th term equal to 46, we have:

Solving for :

So, there are terms in the series.

To find the sum of the series, we use the formula for the sum of an arithmetic series:

where is the number of terms, is the first term, and is the last term . Plugging in the values we found:

Thus, the sum of the series is .