A certain bacteria grows at a rate of 3 cells every 2 minutes. If there were 260 cells initially, how many are there after 21 minutes?

Question

A certain bacteria grows at a rate of 3 cells every 2 minutes. If there were 260 cells initially, how many are there after 21 minutes? ( geometric sequence )

Answer 1

Since the cells grow by addition - "a rate of 3 cells every 2 minutes - this is an arithmetic sequence.

 

a_n = a₁ + (n - 1)d

a₂₁ = 260 + (21/2 - 1)3

a₂₁ = 260 + (10.5 - 1)3

a₂₁ = 260 + (9.5)3

a₂₁ = 260 + 28.5

a₂₁ = 288.5

 

Of course you cannot have a half of a bacteria, so I would say 288.