Question

Derive the formula for the sum of n term of an AP

Answer 1

Step-by-step explanation:

nth term of AP = a+ (n-1) d

Answer 2

Step-by-step explanation:

Sum = a + (a + d) + (a + 2d) + (a + 3d)…+ (l – 3d) + (l – 2d) + (l – d) + l

Where l = a + (n – 1)d

In reverse order, the sum remains the same:

Sum = l + (l – d) + (l – 2d) + (l – 3d) + … (a + 3d) + (a + 2d) + (a + d) + a

Adding equations a and b, we get:

2 x Sum = (a + l) + [(a +d) + (l – d)] … + [(l – d) + (a + d)] + (l + a)]

2 x sum = (a + l) + (a + l)…+ (a + l) + (a + l)

2 x sum = n x (a + l)

sum =

formula for sum of n terms

Substituting l with the previous equation above (where l = a + (n – 1)d):

Sum of n terms of AP =

sum of n terms of ap