Question

Mitosis is a process by which 1 cell divides and becomes 2 cells, those 2 cells divide and become 4 cells, and so on. Write an equation for the nth term of the geometric sequence giving the numbers of cells at each stage of this process, where a1=1. Then find a10.

Answer 1

An equation for the nth term is aₙ = 2ⁿ⁻¹

and a₁₀ = 512

Explanation:

From the question, 1 cell divides and becomes 2 cells, those 2 cells divide and become 4 cells, and so on

∴The sequence will be

1,2,4, ..., n

From the formula

aₙ = a₁rⁿ⁻¹

Where aₙ is the nth term

a₁ is the first term

n is the number of terms

and r is the common ratio

From the sequence,

a₁ = 1,

r = a₂/a₁ = 2/1 = 2

∴ The nth term (aₙ) will be

aₙ = (1)(2)ⁿ⁻¹

aₙ = 2ⁿ⁻¹

Hence, an equation for the nth term is aₙ = 2ⁿ⁻¹

To find a₁₀, substitute n= 10 into the equation

aₙ = 2ⁿ⁻¹

Then

a₁₀ = 2¹⁰ ⁻ ¹

a₁₀ = 2⁹

a₁₀ = 512

∴ a₁₀ = 512