What is the 17th term in the arithmetic sequence -1, -101, -201, -301...

I assume that the question is to prove that; a/(b + c), b/(c +a) and c/(a + b) are in an A.P

Step-by-step explanation:

It is given that a^2 , b^2 and c^2 are in an AP

So they have a common difference

b^2 - a^2 = c^2-b^2

(b - a)(b + a) = (c - b)(c + b)

(b - a) / (b + c) = (c - b) / (b + a)

Let;

(b - a) / (b + c) = (c - b) / (b + a) = K

Now for a/(b + c) , b/(c + a) and c/(a+ b)

b/(c+a) - a/(b+c)

= b(b+c) - a(a+c) / (b+c)(c+a)

= b^2 + bc - a^2 - ac / (b+c)(c+a)

= (b-a)(b+a) + c(b-a)

= (b-a)(b+a+c) / (b+c)(c+a)

= K(a+b+c) / (c+a)

c/(a+b) - b/(c+a)

= c^2 + ac - ab - b^2 /

= (c-b)(c+b) + a(c-b)

= (c - b)(a+b+c) / (a+b)(c+a)

= K(a+b+c) / (c+a)

So;

b/(c+a) - a/(b+c) = c/(a+b) - b/(c+a)

Which means that terms a/(b+c) , b/(c+a) and c/(a+b) have a a common difference

Therefore a/(b+c) , b/(c+a) and c/(a+b) are in an A.P

i can answer this question sweetie!

step-by-step explanation:

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 !