Question

Can someone explain to me how to find the missing terms and common ratio of question #7, and how to answer #8 please

Answer 1

7. general term of gp is given by ar^n-1
hence,4th term is given by

ar^3=15 ------(1)
ar^6=405-----(2)

equation 2/1,we get
r^3=27
so common ratio r=3
putting value of r in equation 1,
we get a=5/9

so gp upto 7 terms will be 5/9,5/3,5,15,45,135,405

8. a=3
given 4th term is -24
so ar^3=-24

substituting value of a we get r^3=-8
r^3= -2^3
so r = -2

using this x2 is ar= 3*-2=-6
           
               x3 is ar^2= 3*4=12