Finding Geometric progression with 2 non-consecutive terms

a Geometric Progression has 2nd term of -1 and the 5th term is 768, find the common ratio and the first term,

i dont know how to do find the common ratio since the terms are not consecutive

Geometric sequences have the form a, a*r, a*r^2, a*r^3...a*r^(n-1)...

Term 2 = ar = -1
Term 5 = ar^4 = 768

a = -1/r

Then ar^4 = -r^3 = 768 = 4^4 * 3

r = -cubert[768] {common ratio}

a = 1/cubert[768] {first term}

a 2 = a r = -1

a 5 = a r^4 = 768

a 5 / a 2 = r^3

so, r^3 = 768 / (-1) = -(768)

hence

r = - cube root (768)

= - 9.16

]so, a2 = a*r = - 9.16 a

- 9.16 a = -1

a = 1/9.16

= 0.11

so

r = - 9.16

a = 0.11