If the sum of first m terms of an A.P. is n and sum of first n terms of the same A.P. is m, show that sum of first (m + n) terms of it is -(m + n).
AP GP
76 Likes

Question

If the sum of first m terms of an A.P. is n and sum of first n terms of the same A.P. is m, show that sum of first (m + n) terms of it is -(m + n).

KnowledgeBoat · Accepted Answer

Let a be the first term and d be common difference of the A.P. Given, Sum of first m terms of an A.P. is n. ⇒ S_m = n ⇒ ⇒ m[2a + (m - 1)d] = 2n ⇒ 2am + m(m - 1)d = 2n ..........(1) Sum of first n terms of an A.P. is m. ⇒ S_n = m ⇒ ⇒ n[2a + (n - 1)d] = 2m ⇒ 2an + n(n - 1)d = 2m ..........(2) Subtracting eq. (2) from (1), we get S_{m + n} = = = [From (3)] = -(m + n). Hence, proved that sum of first (m + n) terms of it is -(m + n).

Mathematics

If the sum of first m terms of an A.P. is n and sum of first n terms of the same A.P. is m, show that sum of first (m + n) terms of it is -(m + n).

AP GP

Related Questions

Find the sum of terms of the A.P. : 4, 9, 14, ……, 89.

3^rd term of a G.P. is 27 and its 6^th term is 729; find the product of its first and 7^th terms.

Find 5 geometric means between 1 and 27.

Mathematics

If the sum of first m terms of an A.P. is n and sum of first n terms of the same A.P. is m, show that sum of first (m + n) terms of it is -(m + n).

AP GP

Related Questions

Find the sum of terms of the A.P. : 4, 9, 14, ……, 89.

Daya gets pocket money from his father every day. Out of the pocket money, he saves ₹ 2.75 on first day, ₹ 3.00 on second day, ₹ 3.25 on third day and so on. Find :(i) the amount saved by Daya on 14th day(ii) the amount saved by Daya on 30th day(iii) the total amount saved by him in 30 days.

3rd term of a G.P. is 27 and its 6th term is 729; find the product of its first and 7th terms.

Find 5 geometric means between 1 and 27.

3^rd term of a G.P. is 27 and its 6^th term is 729; find the product of its first and 7^th terms.