Question

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

Answer 1

first of all we have the 5th term and 2nd term

T5=768 =a*r^4

T2=-12=a*r ^1

make a subject of formula in the both equations

that is a=T2/r and T5/r^4

a=12/r and a=768/r^4

when u equate them u will get

-64=r^3 so r=-4 then to find a that is 1st term

since second term is T2=a*r=12 an r=-4 then

a=12/-4 hence a=-3