WebMar 30, 2024 · We know that Sn = n/2 ( 2a + (n 1)d ) Where, Sn = sum of n terms of A.P. n = number of terms a = first term and d = common difference Thus, Sum of n terms = Sn = /2 (2a + (n 1)d) And Sum of m terms = Sm = /2 (2a + (m 1)d) It is given that, ratio of the sums of m and n terms of an A.P. is m2: n2 (Sum of m terms )/ (Sum of n terms) = m2/n2 (Sm )/ … WebOct 21, 2024 · Best answer Given: Sn = n2p and Sm = m2p To Prove: Sp = p3 We know that, ⇒ 2mp = 2a + (m – 1)d ⇒ 2mp – (m – 1)d = 2a … (ii) From eq. (i) and (ii), we get ⇒ 2np – (n – 1)d = 2mp – (m – 1)d ⇒ 2np – nd + d = 2mp – md + d ⇒ 2np – nd = 2mp – md ⇒ md – nd = 2mp – 2np ⇒ d (m – n) = 2p (m – n) ⇒ d = 2p … (iii) Putting the value of d in eq. (i), we get
If ${S_m} = {S_n}$ for some A.P, then prove that ${S_{m + n}} = 0$.
WebJul 26, 2024 · answered Jul 26, 2024 by Gargi01 (50.9k points) selected Aug 30, 2024 by Haifa Best answer Let the first term of the AP be a and the common difference be d Given: Sm = m2p and Sn = n2p To prove: Sp = p3 According to the problem (m - n)d = 2p (m - n) Now m is not equal to n So d = 2p Substituting in 1st equation we get Hence proved. WebLet us learn all about the sum of n terms of an AP in this article. 1-to-1 Tutoring. Math Resources. Resources. Math Worksheets. Math Questions. Math Puzzles. Math Games. Math Formulas. Calculators. Multiplication … earth bauble
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