Find the next three terms of the sequence -8, 24, -72, 216, . . .?

Solution:

Given sequence is -8, 24, -72, 216, . . .

Common ratio r = t₂/ t₁ = 24/ -8 = -3

Also t₃/t₂ = -72/24 = -3

The given sequence is a Geometric sequence.

The general term nth term of the geometric sequence is given by:

a_n = a · r^{n - 1}

Where a and r being the first term and the common ratio respectively.

Here, a₁ = a = -8 and r = -3

Next three terms are:

a₅ = a · r^{5 - 1} = (-8)×(-3)⁴ = -648

a₆ = a · r^{6 - 1} = (-8)×(-3)⁵ = 1944

a₇ = a · r^{7 - 1} = (-8)×(-3)⁶ = -5832

Find the next three terms of the sequence -8, 24, -72, 216, . . .?

Summary:

The next three terms of the sequence -8, 24, -72, 216, . . . are -648, 1944 and -5832.