find the 100th and the nth term for the following sequence. show work.
a. 197+7 x 3^27, 197+8 x 3^27, 197+9 x 3^27

nth term of this sequence is

and 100th term is .

Step-by-step explanation:

The given sequence is

Now we will find the difference between each successive term.

Second term - First term =

                                         =

                                         =

                                         =

Similarly third term - second term =

So there is a common difference of .

It is an arithmetic sequence for which the explicit formula will be

=a + (n - 1)d

where = nth term of the arithmetic sequence

where a = first term of the arithmetic sequence

n = number of term

d = common difference in each successive term

Now we plug in the values to get the 100th term of the sequence.

               =

                   =

                   =

Therefore, nth term of this sequence is

and 100th term is .

18.75 gallons

step-by-step explanation: