Question

The 3rd term of a geometric sequence is -1/3 and the 8th term is 81. what is the 11th term?

Answer 1

Answer: $t_{11}=-2187$

Step-by-step explanation:

$t_{3}=-1/3$

That is :

$ar^{2} = -1/3$ ................. equation 1

Also

$t_{8}=81$

that is

$ar^{7}=81$ ................. equation 2

divide equation 2 by equation 1 , that is

$\frac{ar^{7}}{ar^{2}} = 81 / -1/3$

$r^{5}=$ $81$ x $-3/1$

$r^{5}= -243$

find the fifth root of both sides

$r = -3$

substitute $r = -3$ , into equation 1 to find a , that is

$a(-3^{2})= -1/3$

$9a = -1/3$

multiply through by 3

$27a = -1$

$a =- 1/27$

To find the 11th term , the formula for the 11th term is given as :

$t_{11}=ar^{10}$

$t_{11}= -1/27(-3^{10})$

$t_{11}=-2187$