Class10 ncert Ex 9.2,16,

Hi Ashwini

In Ex 9.2, 16 of Class 11,

We are inserting numbers between two numbers, 

So, the formula is d = (b - a)/(n + 1)

Derivation:

Q: Insert 2 numbers between 1 & 4 so that it is an AP

Let a = 1, b = 4

Now,

1, a1, a2, 4 is an AP

So, Last term = a + (n - 1)d

Where n = total number of terms = 4

a = First term = 1

4 = 1 + (4 - 1)d

4 = 1 + 3d

4 - 1 = 3d

3 = 3d

d = 3/3

d = 1

Now, let m = Number of terms to be inserted = 2

d = (b - a) / m + 1

d = (4 - 1) / 2 + 1

d = 3/3

d = 1

That is the rough derivation.