Question

Find an equation for the nth term of a geometric sequence where the second and fifth terms are -2 and 16, respectively.

a_n = 1 • (-2)n - 1

a_n = 1 • 2n

a_n = 1 • (-2)n + 1

a_n = 1 • 2n - 1

Answer 1

nth term of a geometric sequence is: \(\large a_n = ar^{n-1}\) ----- (1)
\(\large a_2 = ar^{2-1} = ar = -2\) ----- (2)
\(\large a_5 = ar^{5-1} = ar^4 = 16\) ----- (3)

Divide (3) by (2) and solve for 'r':
Then put 'r' in (2) and solve for 'a'

Put 'a' and 'r' in (1).