Question

Identify the 8th term of the geometric sequence in which a2 = 768 and a4 = 48.

Answer 1

3/16

Explanation:

Let r = constant ratio

a_2 = 768

a_3 = 768r

a_4 = 48

768r/768 = 48/768r

r = 1/(16r)

16r² = 1

r² = 1/16

r = 1/4

a_n = a_1 × r^(n - 1)

a_2 = a_1 × (1/4)^1

768 = a_1 × 1/4

a_1 = 3072

a_8 = a_1 × r^(8 - 1)

a_8 = 3072 × (1/4)^7

a_8 = 3072/16384

a_8 = 3/16