For Daily Free Study Material Join wiredfaculty Whatsapp Group | Download Android App | Ncert Book Download
Permutations And Combinations
If the sum of first n terms of a sequence is of the form An2 + Bw, where A and B arc constants (independent of n). Show that the sequence is an A.P. Is the converse true? Justify your answer.
Here, ...(i)Replacing n by (n - 1) in (i), we get = ...(ii) = Replacing n by (n - 1) in (iii), we get Now, which is independent of n
∴ The sequence is an A.P.Yes, the converse is true.Let a be the first term and d be the common difference.
∴ where and are fixed numbers.Hence, if the sequence is an A.P. then the sum of first n terms must be of the form