Given the sequence 8, 16, 32, 64, ..., which expression would give the thirteenth term?

Solution:

Given,

The sequence 8, 16, 32, 64, ...,

First term = 8, Common ratio = 16/8 = 32/16 = 2

We know that,

a_n = a₁r^{n - 1}.

a₁₃ = 8 . 2¹²

a₁₃ = 8(4096)

a₁₃ = 32768.

So, the sequence is a₁, a₂, ...... a₁₃ ......a_n

⇒  8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768,....

Therefore, a₁₃ = 32768.

Given the sequence 8, 16, 32, 64, ..., which expression would give the thirteenth term?

Summary:

Given the sequence 8, 16, 32, 64, ..., the expression that would give the thirteenth term of the sequence is a₁₃ = 32768.