If the sum of first 7term of an AP is 49 and that of 17term is 289 , find the sum of first n terms

If the sum of first 7term of an AP is 49 and that of 17term is 289 , f

1.	If the sum of first 7term of an AP is 49 and that of 17term is 289 , find the sum of first n terms
Answer» n2 Given that,S7\xa0= 49S17\xa0= 289S7\xa0=\xa07/2\xa0[2a\xa0+ (n\xa0- 1)d]S7\xa0= 7/2\xa0[2a\xa0+ (7 - 1)d]49 = 7/2\xa0[2a\xa0+\xa016d]7 = (a\xa0+ 3d)a\xa0+ 3d\xa0= 7 ...\xa0(i)Similarly,S17\xa0= 17/2\xa0[2a\xa0+ (17 - 1)d]289 = 17/2 (2a\xa0+ 16d)17 = (a\xa0+ 8d)a\xa0+ 8d\xa0= 17 ...\xa0(ii)Subtracting equation\xa0(i)\xa0from equation\xa0(ii),5d\xa0= 10d\xa0= 2From equation\xa0(i),a\xa0+ 3(2) = 7a +\xa06 = 7a =\xa01Sn\xa0=\xa0n/2\xa0[2a\xa0+ (n\xa0- 1)d]=\xa0n/2\xa0[2(1)\xa0+ (n\xa0- 1)\xa0× 2]=\xa0n/2 (2\xa0+ 2n\xa0- 2)=\xa0n/2 (2n)=\xa0n2\xa0