Given: x-1;x+1;x...as the first 3 terms of a geometric sequence 1.1 Determine the value (s)of x
1.2 Hence, or otherwise, find the common ratio of the sequence
1.3why is the sequence convergent​

see explanation

Step-by-step explanation:

(1)

The common ratio r of a geometric sequence is

r = = , so

= ( cross- multiply )

(x + 1)² = x(x - 1) ← expand both sides

x² + 2x + 1 = x² - x ( subtract x² - x from both sides )

3x + 1 = 0 ( subtract 1 from both sides )

3x = - 1 ( divide both sides by 3 )

x = -

(2)

r = = = = -

(3)

If - 1 < r < 1 then the sequence will converge

r = - meets this criteria , thus the sequence is convergent

answer:     true

step-by-step explanation: