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4 x 416er every question. Each question carries 4 marks.A) The sum of the three terms which are in A.p. is 33. If the product of thefirst and the third terms exceeds the second term by 29. Find the A.p. |
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Answer» First term = aCommon difference = d Given,Sum of the first three terms = 33 Second term = a + dthird term = a + 2d 33 = a + a + d + a + 2d33 = 3a + 3d33 = 3 ( a + d ) 11 = a + d d = 11 - a Given, Product of first and third term exceeds second term by 29 a1 × a3 = a2 + 29 a × a + 2d = a + d + 29 a² + 2 ad = a + d + 29 a² + 2ad - a - d = 29 a² + 2a ( 11 - a) - a - (11 - a) = 29 a² + 22a - 2a² - a - 11 + a = 29 - a² + 22a - 11 = 29 - a² + 22a - 11 - 29 = 0 - a² + 22a - 40 = 0 a² - 22a + 40 = 0 Splitting the middle term a² - 20 a - 2a + 40 = 0 (a² - 20a) - (2a - 40) = 0 a ( a - 20) - 2 (a - 20) = 0 ( a - 2) ( a -20) = 0 a - 2 = 0a = 2 a - 20 = 0a = 20 Case - 1 a = 2 d = 11 - a = 11 - 2 = 9 A.P = 2 , 11 , 20 ... Case - 2 a = 20d = 11 - a = 11-20 = -9 A.P = 20 , 11 , 2 ... |
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