If the mth term of and AP is a and nth term of AP is b.Show that the sum of m+n is:- [{m+n/2}]a+b+{a-b/m-n}

Asked by Udit Lilhare | 29th Jan, 2014, 04:58: PM

Expert Answer:

Let a' and d respectively be the first term and common difference of the AP. Here, mth term is a. So, a' + (m - 1) d = a ... (1) And, nth term is b. So, a' + (n - 1) d = b ... (2) Subtracting (2) from (1), we have: (m - n)d = a-b So, d = (a-b)/(m-n) Now, find the value of a by substituting the value of d in any of the above two equations (1) or (2). Now, sum of (m+n) terms = (m+n)/2 [2a' + (m+n-1)d] Now, substitute the values of a' and d to get the answer.

Answered by  | 29th Jan, 2014, 05:21: PM

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