Tutor profile: Maharnab M.

What is the sum of the sequence 2,4,6,8,.... upto 10 terms?

The given series is an AP (arithmetic progression) with first term a=2 and common difference=2. Sum of an AP upto n terms is given by $$\frac{n}{2} [2a+(n-1)d]$$ Here, n=10. So, plugging in the values we get: Required sum = $$\frac{10}{2} [2(2)+(10-1)2]=110$$

What is the sum of the exterior angles of a triangle?

Let the values of the interior angles of a triangle be x, y and z respectively. So, x+y+z=$$180^{o}$$ The exterior angles are given by $$(180^{o}-x), (180^{o}-y),(180^{o}-z)$$ $$\implies (180^{o}-x)+(180^{o}-y)+(180^{o}-z)= 3 \times 180^{o}-180^{o} = 360^{o}$$ So, the sum of the exterior angles of a triangle is 360 degrees.

What is the sum of the first 10 natural numbers?

The sum of first n natural numbers is given by n(n+1)/2. So, the sum of the first 10 natural numbers will be 10(10+1)/2 = 55