How do you find a general formula for each arithmetic sequence given 8th term is -20; 17th term is -47?

1 Answer
Feb 20, 2016

Answer:

#n^(th)# term of the arithmetic sequence is given by #4-3n#

Explanation:

If #a# is the first term of an arithmetic sequence and #d# the difference between a term and its preceding term, general formula for #n^(th)# term of the arithmetic sequence is given by #a+(n-1)d#.

As #8^(th)# term is #-20# and #17^th# term is #-47#

#a+(8-1)d=a+7d=-20# and #a+(17-1)d=a+16d=-47#.

Subtracting first equation from second, we get

#9d=-47+20# or #9d=-27# i.e. #d=-3#

putting this in first we get #a+7*(-3)=-20# or #a=1#.

Hence, #n^(th)# term of the arithmetic sequence is given by #1-3(n-1)# or #4-3n#