Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -12 and 768, respectively

Nth term is given by

Step-by-step explanation:

For a geometric progression we have expression for nth term

where a is first term and r is common ratio.

Here the second and fifth terms are -12 and 768.

That is

           a₂ = ar²⁻¹ = ar = -12

           a₅ = ar⁵⁻¹ = ar⁴ = 768

Dividing we will get

Substituting in

          ar = -12

          a x -4 = -12

          a = 3

Nth term is given by

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.