Find the geometric means in the following sequence. –6, ? , ? , ? , ? , –1,458?

The sequence is,

-6, -18, -54, -162, - 486, -1458, -4374

Step-by-step explanation:

It is given a geometric sequence,

–6, ? , ? , ? , ? , –1,458?

From the given sequence we get first term a₁ = -6 and 6th term a₆ = -1458

To find the common ratio 'r'

6th term can be written as

a₆ = ar⁽⁶ ⁻ ¹⁾

-1458 = 6 * r⁽⁶⁻¹⁾

r⁵ = -1458/-6 = 243

r = ⁵√243 = 3

To find the sequence

We have a = -6, r = 3

a₂ = -6 * 3 = -18

a₃ = a₂*3 = -18* 3 = -54

a₄  = a₃*3 = -54 * 3 = -162

a₅ = a₄*3 = -162* 3 = -486

a₆ = - 1458

a₇ = a₂*3 =-1458 * 3= -4374

The sequence is,

-6, -18, -54, -162, - 486, -1458, -4374