Question

In the pattern shown below Day 1 has 4 night eyes,

followed by Day 2 with 8 night eyes, and Day 3 with 16
night eyes, how many eyes will there be on Day 25?
Explain using words or numbers a pattern that you see in
the picture below and write it in complete sentences.

Answer 1

The pattern that we know is:

D₁ = 4 night eyes

D₂ = 8 night eyes

D₃ = 16 night eyes

Ok, with these 3 elements we can see that this seems like a geometric sequence.

How we test it? well, the quotient between any pair of consecutive terms must be constant.

D₂/D₁ = 8/4 = 2

D₃/D₂ = 16/8 = 2

Then we can write the n-th term as:

Dₙ = D₁*2^(n-1) = 4*2^(n-1)

Then in day 25, we have n = 25.

Then the term is:

D₂₅ = 4*2^(24) = 67,108,864 night eyes