Math, asked by divyaram34892, 8 months ago

Write the sum of 10 A.M.'s inserted between a and b.​

Answers

Answered by sadiqanoori10082010
2

Answer:

Let, a and b two given numbers.

Let,

A

1

,A

2

,A

3

.............A

n

be Arithmetic means between a and b.

a,A

1

,A

2

,A

3

.............A

n

,b are in A.P.

a+A

1

+A

2

+A

3

+......A

n

+b=(

2

n+2

)(a+b) (first term is =a, last term=b, number of term=n+2)

A

1

,A

2

,A

3

.............A

n

=

2

(n+2)(a+b)

−(a+b)

=(a+b)[

2

n+2

−1]

=(a+b)[

2

n+2−2

]

=n(

2

a+b

)

= n times the single A.M. Between a and b

Hence, this is the answer.

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