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44. If S,, S2 and S3 are the sum of n, 2n and3n terms of an Arithmetic Progression(A.P.) then which one of the following istrue:(I) S3 S2 +S (2) S3 3 (S2-S1)(3) S3 2 (S2-S) (4) S3 4 (S, -S,) |
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Answer» Option- B Let ‘a’ be the first term of the AP and ‘d’ be the common differenceS1= (n/2)[2a + (n – 1)d] --- (1)S2= (2n/2)[2a + (2n – 1)d] = n[2a + (n – 1)d] --- (2)S3= (3n/2)[2a + (3n – 1)d] --- (3) Consider the RHS: 3(S2– S1)Substitute the values of S2and S1and simplify to get the LHS |
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