The Total solution for NCERT class 6-12
Let a, a + d, a + 2d,a + 3d, тАжтАж.. be an A.P.an┬а= a + (n тАУ 1) d10th (a10) = a + (10 тАУ 1) d = a + 9dand 24th term (a24) = a + (24 тАУ 1) d = a + 23d24th term = 2 x 10th terma + 23d = 2 (a + 9d)=> a + 23d = 2a + 18d=> 2a тАУ a = 23d тАУ 18d=> a = 5d тАж.(i)Now 72nd term = a + (72 тАУ 1)d = a + 71dand 34th term = a + (34 тАУ 1) d = a + 33dNow a + 71d тАУ 5d + 71d = 76dand a + 33d = 5d+ 33d = 38d76d = 2 x 38d72th term = 2 (34th term) = twice of the 34th termHence proved.