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age wl be WU TIlQ.15 If an AP consists of n terms with first term a and nh term i. Show that the sum of the mterm form the beginning and mth term from the end is (a +),in ordet are ( A(35 3.-2) and |
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Answer» First term of A.P is anth term =lLet d be the common differencenth term=a+(n-1)dl=a+(n-1)dd=l-a/n-1 ------------1 Mth term from the beginning=a+(m-1)d=a+(m-1)(l-a/n-1 ) ----------------2 Mth term from the end we get:where we consider first term as l and the common difference=-d=l+(m-1)(-d)=l+(m-1)x(-(l-a)/n-1)=I-(m-1)(l-a)/n-1 --------------3 thus sum of mth term from beginning to end is=a+(m-1)(l-a/n-1 ) +I-(m-1)(l-a)/n-1=a+lHence proved |
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