Question

Write the explicit formula for the geometric sequence.

a1 = -5 a2 = 20 a3 = -80

Answer 1

(an) is a geometric sequence if a(n+1) = q . a(n), q is not zero, that means
a(n+1) / a(n) = q, consenquently we can find q, a2/a1=a3/a2= - 4 = q,
the main expression of the geometric sequence is given by
a(n) = q^(n-p) . a(p), p is the index of the first term, in this case p=1, so
a(n) = q^(n-1) . a(1), finally the explicit formula is
a(n) = (- 4)^(n-1) . (-5)