Question

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

Answer 1

`a_n=486(-1/3)^(n-1)`

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)`