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If the sum of first 7 terms of an APis 49and that of 17 terms is 289, find the sumof first n terms. (Problem Solving) |
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Answer» S7= 49S17= 289S7 =7/2[2a+ (n- 1)d]S7= 7/2[2a+ (7 - 1)d]49 = 7/2[2a+16d]7 = (a+ 3d)a+ 3d= 7 ...(i)Similarly,S17= 17/2[2a+ (17 - 1)d]289 = 17/2 (2a+ 16d)17 = (a+ 8d)a+ 8d= 17 ...(ii)Subtracting equation(i)from equation(ii),5d= 10d= 2From equation(i),a+ 3(2) = 7a +6 = 7a =1Sn=n/2[2a+ (n- 1)d]=n/2[2(1)+ (n- 1)× 2]=n/2 (2+ 2n- 2)=n/2 (2n)=n² |
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