Question

If there are 'n' arithmetic means between 'a' and 'b', then d=

A) ab/n+1

B) n+1/b+a

C) b-a/n+1

D) b+a/n+1

Answer 1

HELLO DEAR,


LET a1,a2,.......,an BE n ARITHMETIC MEAN


a,a1,a2,.......,an,b ARE in A.PNo OF TERMS



=n+2let d BE THE COMMON DIFFERENCE.

,


b=a+(n+2−1)db−a=(n+1)d⇒d=b−an+1




$b = a + (n + 2 - 1)d \\ = > b - a = (n + 1)d \\ = > d = \frac{(b - a)}{(n + 1)}$


I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Answer:

Step-by-step explanation:

1. Let A1, A2,A3,......so on An be 'n' arithmetic means between a and b.

2. Here we see that a, A1,A2,A3,......,b are in AP.

3. Then,

nth term= a+(n-1)d

4. Here, nth term=b

a=a

n= n+2 (because there are total n Arithmetic means and 'a' and 'b'.

5. Now,

b=a+(n+2-1)d

b-a=(n+1)d

b-a/n+1=d

So we got option C.