the 5th term of a geometric sequence is 144 and the 10th term is 4608. find the first term and common difference

First term = 9.

Common ratio = 2.

Step-by-step explanation:

A geometric sequence has a common ratio r.

If the first term is a:

10th term = ar^9 and 5th term is ar^4

so 1th term / 5th term = r^5

So 4608/144 = r^5

r^5 = 32

so r = 2.

Substituting for r in the 5th term:

a(2)^4 = 144

a = 144 / 16

a = 9.

first term:9

common ratio: 2

Step-by-step explanation:

aₙ = a₁*rⁿ⁻¹

a₅ = a₁*r⁵⁻¹ = a₁*r⁴ = 144  ... (1)

a₁₀ = a₁*r¹⁰⁻¹ = a₁*r⁹ = 4608  ... (2)

(2)÷(1)  r⁵ = 32

r = 2

a₁ = 144 / 2⁴ = 9

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !