If A1- A2- A3- - An are n numbers between a and b- such that a- A1- A2- A3- - An- b are in A-P- then the common difference of this A-P- is-A- b-a-n-2B- b-a-n-1C- b-a-nD- b-a-n-1

The correct option is D nbsp; nbsp; Let common difference be d. Here, first term = a, total number of terms = (n + 2) nbsp; nbsp; ...

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Sum of n Terms

If A1, A2, A3...

Question

If A₁, A₂, A₃,...., A_n are n numbers between a and b, such that a, A₁, A₂, A₃,..., A_n, b are in A.P., then the common difference of this A.P. is:

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a_{1}, a_{2}, a_{3}, . . . . . a_{2 n}

\frac{a_{1} + a_{2 n}}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{a_{2} + a_{2 n - 1}}{\sqrt{a_{2}} + \sqrt{a_{3}}} + \frac{a_{3} + a_{2 n - 2}}{\sqrt{a_{3}} + \sqrt{a_{4}}} + . . . + \frac{a_{n} + a_{n + 1}}{\sqrt{a_{n}} + \sqrt{a_{n + 1}}} =

a_{1}

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A . P .

\frac{1}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{1}{\sqrt{a_{2}} + \sqrt{a_{3}}} + . . . + \frac{1}{\sqrt{a_{n - 1}} + \sqrt{a_{n}}} = \frac{(n - 1)}{\sqrt{a_{n}} + \sqrt{a_{1}}}

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