The first term of a geometric sequence is 5, and the third term is 16/5. How do you find the fifth term?

1 Answer
Dec 9, 2015

Answer:

fifth term is #256/125#

Explanation:

For a geometric sequence
#color(white)("XXX")a_(i+1) = a_i*r # for #i > 1# and some constant #r#
#color(white)("XXX")a_(i+2) = a_i*r^2#

Given
#color(white)("XXX")a_1 = 5#
and
#color(white)("XXX")a_3=16/5#

#color(white)("XXX")=5*r^2#

#color(white)("XXX")r^2= 16/25#

#color(white)("XXX")r^4= (16^2)/(25^2)#

#color(white)("XXX")a_5 = a_1*r^4 = (cancel(5)*16^2)/(cancel(25)_5*25) = 256/125#