How do you find nth term rule for #375,-75,15,-3,....#?

1 Answer
Nov 20, 2016

Answer:

#a_n=375 *(-1/5)^(n-1)#

Explanation:

Find the nth term rule for: #375, -75, 15, -3#...

If you divide any term by the previous term, the quotient is #-1/5#

This indicates the sequence is geometric. In other words, the next term is generated by multiplying the previous term by a fixed number called the common ratio or #r#.

The "formula" for a geometric sequence is #a_n=a_1 * r^(n-1)# where #r# is the common ratio, #a_1# is the first term in the sequence, and #n# is the number of the term in the sequence.

In this example, #r= -1/5# and #a_1 = 375#

#=> a_n=375 *(-1/5)^(n-1)#