What is the first term of the geometric sequence presented in the table below? n 4 9 an 6 −192 hint: an  = a1(r)n − 1, where a1 is the first term and r is the common ratio.

The equation for the n-th term of the geometric sequence is

where
a₁ =  the first term
r = the common ratio.

a₄ = 6, therefore
a₁ r³ = 6                      (1)

a₉ = -192, therefore
a₁ r⁸ = -192                 (2)

Divide equation (2) by equation (1).


From (1), obtain
a₁(-2)³ = 6
-8a₁ = 6
a₁ = -3/4

-3/4