# How do you write the expression for the nth term of the geometric sequence #a_4=-18, a_7=2/3, n=6#?

##### 1 Answer

Mar 5, 2017

#### Explanation:

#"The nth term for a geometric sequence is"#

#• a_n=ar^(n-1)" where a is the 1st term"# To obtain the nth term for the given sequence, we require to find a and r.

#"Given " a_4=-18" and "a_7=2/3" then"#

#rArra_4=ar^3=-18to(1)#

#rArra_7=ar^6=2/3to(2)#

#rArr(ar^6)/(ar^3)=(2/3)/(-18)#

#rArrr^3=-1/27rArrcolor(red)(r=-1/3)#

#"From (1) " ar^3=-18#

#rArra=(-18)/(-1/27)rArrcolor(red)(a=486)#

#rArr"nth term expression is " a_n=486(-1/3)^(n-1)#