Question

please send me the answer with steps

Answer 1

Before we can figure out the 100th term, we need to find a rule for this arithmetic sequence. Remember, the general rule for this sequence is

where  represents the first number in the sequence,  is the common difference between consecutive numbers, and is the -th number in the sequence.  

In our problem, . Also, each time we move up from one number to another, the number increases by 7.  Therefore,.  So the rule for this sequence is written as

Now that we found our rule, we can go on and figure out what the 100th term is equal to.  For the 100th term.