How do you find #a_100# when #a_1=-30#, d=5?

1 Answer
Aug 1, 2017

Answer:

#a_100=465#

Explanation:

Since this problem uses #d#, the common difference, we know this is an arithmetic sequence.

The general formula for an arithmetic sequence is #a_n=a_1+(n-1)d#, where #a_n# is the #n^(th)# term, #a_1# is the first term, and #d# is the common difference.

Since we already know that #a_1=-30# and #d=5#, we can substitute these values into the formula.

#a_n=a_1+(n-1)d#

#a_n=-30+(n-1)5#

To find #a_100#, substitute #100# for #n#.

#a_100=-30+(100-1)5#

Now, we can simplify.

#a_100=-30+(99)(5)#

#a_100=-30+495#

#a_100=465#