Question 126680
Question:

determine the common ratio of a geometric sequence whose first term is 2 and whose fourth term is 16?


Answer,

The nth term of a geometric series is given by the formula,

n th term = {{{ a(r)^(n-1)}}}, where r is the common ratio and a is the first term.


So, fourth term = {{{ a(r)^3}}}


here first term is given as 2and fourth term is 16.


so,  16 = {{{ 2(r)^3}}}


divide both sides by 2


==> 16/3 = {{{ (2(r)^3)/2}}}


==> 8 = {{{r^3}}}


==> {{{ 2^3 = r^3}}}


==> {{{ 2 = r }}}



That is common ratio is 2.



Hope you found the explanation useful.


Regards.


Praseena.