WebS(m+n)=(m+n)/2*[2a+(m+n-1)d] Now substitute the value of 2a and d we got earlier in the above eqn- You will get- (m+n)/2*[2n*n+2m*m+2mn-2m-2n-2m*m-2n*n-4mn+2m+2n]/mn..... The final eqn you get on simplification is- (m+n)/2*(-2mn)/m The Answer is -m-n.... WebSep 1, 2024 · Given; In an A.P, Sm = n and Sn = m, also m > n To Find; the sum of the first ( m-n ) terms. Solution; It is given that In an A.P, Sm = n and Sn = m, also m > n Sn=n2 [2a+ (n−1)d] =m Sm=m2 [2a+ (m−1)d]=n Sn−Sm=n2 [2a+ (n−1)d]−m2 [2a+ (m−1)d] 2 (m−n)=2a (n−m)+ [ (n2−m2)− (n−m)]d−2 (n−m)= (n−m) [2a+ { (n+m)−1}d] Divide (n-m) to both sides.
If in an A.P. the sum of m terms is equal to n and the sum of n …
WebMar 12, 2024 · Let a is the first term and d is the common difference of the ap. Sn = n²p ⇒n/2 [2a + (n -1)d ] = n²p ⇒2a + (n - 1)d = 2np ........ (1) Sm = m²p ⇒m/2 [2a + (m - 1)d ] = m²p ⇒2a + (m - 1)d = 2mp ......... (ii) from equations (1) and (2) we get, [2a + (n - 1)d]/ [2a + (m - 1)d ] = 2np/2mp ⇒ [2a + (n - 1)d ] × m = [2a + (m - 1)d ] × n WebDec 28, 2024 · If in an arthemetic progression sm=n and sn=m, then prove that sm+n=- (m+n). See answers Advertisement abhi178 Let a is the first term and d is the common difference . (m - n) = -2a (m-n)/2 - (m-n) (m+n)/2+ (m-n)d/2 1 = -2a/2 - (m+n)/2 + d/2 1 = -1/2 {2a + (m+n-1)d} --------- (1) from equation (1) S_ {m+n} = - (m+n) hence, proved // … daughtry \u0026 farine attorney
In an A. P., Sm : Sn = m^2 : n^2 The ratio of p^2 th term to …
WebThe partial sum of the infinite series Sn is analogous to the definite integral of some function. The infinite sequence a (n) is that function. Therefore, Sn can be thought of as the anti-derivative of a (n), and a (n) can be thought of like the derivative of Sn. Web1 answers Gaurav Seth 2 years, 3 months ago Let a is the first term and d is the common difference . (m - n) = -2a (m-n)/2 - (m-n) (m+n)/2+ (m-n)d/2 1 = -2a/2 - (m+n)/2 + d/2 1 = -1/2 {2a + (m+n-1)d} --------- (1) from equation (1) S_ {m+n} = - (m+n) 2Thank You ANSWER Related Questions Prove 5^ is irrational WebIf in an A.P., S n = qn 2 and S m = qm 2, where S r denotes the sum of r terms of the A.P., then Sq equals q3. Explanation: The given series is A.P. whose first term is a and common difference is d ∴ S n = n 2 [ 2 a + ( n - 1) d] = qn 2 ⇒ 2a + (n – 1)d = 2qn .... (i) S m = m 2 [ 2 a + ( m - 1) d] = qm 2 ⇒ 2a + (m – 1)d = 2qm ..... (ii) daughtry tyree