How do you write the explicit formula for the sequence 0.5,-0.1,0.02,-0.004...?

1 Answer
Mar 9, 2016

Answer:

Explicit formula for the sequence's #n^(th)# term is #0.5xx(-1/5)^(n-1)#

Explanation:

The sequence #{0.5,-0.1,0.02,-0.004,..}# is a geometric series of the type #{a, a, ar^2, ar^3,....}#, in which #a# - the first term is #0.5# and ratio #r# between a term and its preceding term is #-1/5#.

As the #n^(th)# term and sum up to #n# terms of the series #{a, a, ar^2, ar^3,....}# is #ar^(n-1)# and #(a(1-r^n))/(1-r)# (as #r<1# - in case #r>1# one can write it as #(a(r^n-1))/(r-1)#.

As such #n^(th)# term of the given series #{0.5,-0.1,0.02,-0.004,..}# is #0.5xx(-1/5)^(n-1)#