In an A.P. if m^th term is n and n^th term is m, show that its r^th term is (m + n - r).
AP
66 Likes

Question

In an A.P. if m^th term is n and n^th term is m, show that its r^th term is (m + n - r).

KnowledgeBoat · Accepted Answer

Let first term be a and common difference be d. Given, ⇒ a_m = n ⇒ a + (m - 1)d = n ⇒ a + md - d = n ⇒ a = n - md + d .......(i) Also, ⇒ a_n = m ⇒ a + (n - 1)d = m ⇒ a + nd - d = m Substituting value of a from (i) in above equation, ⇒ n - md + d + nd - d = m ⇒ nd - md = m - n ⇒ d(n - m) = m - n ⇒ d = = -1. Substituting value of d in (i) we get, ⇒ a = n - m(-1) + (-1) = n + m - 1. a_r = a + (r - 1)d = n + m - 1 + (r - 1)(-1) = n + m - 1 - r + 1 = n + m - r. Hence, proved that r^th term is (m + n - r).

Mathematics

In an A.P. if m^th term is n and n^th term is m, show that its r^th term is (m + n - r).

AP

Related Questions

4^th term of an A.P. is equal to 3 times its first term and 7^th term exceeds twice the 3^rd term by 1. Find the first term and the common difference.

The sum of the 2^nd term and the 7^th term of an A.P. is 30. If its 15^th term is 1 less than twice of its 8^th term, find the A.P.

Which term of the A.P. 3, 10, 17, …….. will be 84 more than its 13^th term ?

The sum of 41 terms of an A.P. with middle term 40 is :
820
1640
2460
none of these

Mathematics

In an A.P. if mth term is n and nth term is m, show that its rth term is (m + n - r).

AP

Related Questions

4th term of an A.P. is equal to 3 times its first term and 7th term exceeds twice the 3rd term by 1. Find the first term and the common difference.

The sum of the 2nd term and the 7th term of an A.P. is 30. If its 15th term is 1 less than twice of its 8th term, find the A.P.

Which term of the A.P. 3, 10, 17, …….. will be 84 more than its 13th term ?

The sum of 41 terms of an A.P. with middle term 40 is :82016402460none of these

In an A.P. if m^th term is n and n^th term is m, show that its r^th term is (m + n - r).

4^th term of an A.P. is equal to 3 times its first term and 7^th term exceeds twice the 3^rd term by 1. Find the first term and the common difference.

The sum of the 2^nd term and the 7^th term of an A.P. is 30. If its 15^th term is 1 less than twice of its 8^th term, find the A.P.

Which term of the A.P. 3, 10, 17, …….. will be 84 more than its 13^th term ?

The sum of 41 terms of an A.P. with middle term 40 is :
820
1640
2460
none of these