How do you find the explicit formula for the following sequence 57, 66, 75, 84, 93, ...?

1 Answer
Apr 14, 2016

Answer:

#n_(th)# of the series is given by #9n+48#

Explanation:

As the difference between a term and its preceding term is always #9#, it is an arithmetic sequence of type

#{a,a+d,a+2d,a+3d,a+4d,a+5d,..........}#

If #a# is the first term of such a series and #d# is the difference between a term and its preceding term,

#n_(th)# of the series is given by #a+(n-1)d#.

Here #a=57# and #d=9#, hence

#n_(th)# of the series is given by #57+9(n-1)=9n+48#.