Question

What is the 11th term of the geometric sequence − 1.5, − 3, − 6, − 12, … ?

Answer 1

Consider the geometric sequence,

{− 1.5, − 3, − 6, − 12, …}

 

First term of the sequence is a1 = -1.5

 

Common ratio of the given sequence will be computed as follows:

r = a2 ÷ a1

   = (-3) ÷ (-1.5)

   = 2

 

Use the formula for the nth term of a geometric sequence,

an = a1 × rn-1 ...... (1)

 

Substitute a1 = -1.5, n = 11 and r = 2 in (1) and compute 11th term of the given sequence,

a11 = -1.5 × 211-1

   = -1.5 × 210

   = -1.5 × 1024

   = -1536

 

Therefore, 11th term of the given sequence is a11 = -1536.

Therefore, 11th term of the given sequence is a11 = -1536.