CBSE Class 10 Answered
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 | 29 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 | 29 Jan, 2014, 05:21: PM
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