Answer:
The sequence is,
-6, -18, -54, -162, - 486, -1458, -4374
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