Question

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.

Answer 1

let a2 = b0 and therefore a5 = b3 and solve for the b sequence, then adjust it back to a with an index shift if need be

Answer 2

the idea is to find the common difference to establish what to do in a

Answer 3

@amistre64 I dont understand

Answer 4

a1 = b\(_{(-1)}\)

a2 = b0 = -6
a3 = b1 = -6 + d
a4 = b2 = -6 + d + d
a5 = b3 = -6 + d + d + d = 162

now, depending on how you material starts n, at 0 or at 1 ... then the rule for the sequence is some first term, plus some n (or n-1) multiplies of d.