Question

A turtle population grows in a manner that closely resembles a geometric sequence. Given the table of values, determine the turtle population after 5 years.
Year Number of turtles
1 6
2 18
3 54

Answer 1

The turtle population will be 486 after 5 years.

Step-by-step explanation:

The general form of a geometric progression or geometric sequence is a, ar, ar², ar³ and so on.

where,

• a = first term
• r = common ratio

The formula to find the nth term in GP is :

nth term = $ar^{n-1}$

The given sequence 6,18,54.

In this sequence,

• The first term, a = 6
• The common ratio, r = 18/6 = 3

5th term = $6\times3^{5-1}$

⇒ $6\times3^{4}$

⇒ 6$\times$81

⇒ 486

Therefore, after 5 years the population will be 486.