Question 6 25 marks This question is based on your work on M U123 up to and inciuding Unit 9. (a) (i) For the nite arithmetic sequence 4,9,14,...,69. write down the rst term a, the common difference d and the last term L, and hence nd the number of terms n of the sequence. Check that your answer is correct. (ii) Use an appropriate formula from Unit 9, Subsection 1.1 to nd the sum of the arithmetic sequence in part (a) (i). (b) Expand the brackets in the following expressions. (i) (7:12 5)(3r - 4) (ii) (4o T3302 (c) Factorise 16h2 49332. 2 (d) (i) Factorise the quadratic expression a: 6:1: 55. (ii) Use your answer to part [(1) (i) to solve the quadratic equation 1:2 6:1: 55 0, showing each step in your reasoning. Check that your solution is correct. (e) A student writes down the following piece of work which contains an error in their reasoning. The eczua'tion is: 92' - 2.39 = 0 Add 2.3;; to each side: 32' = 2.39 Divide each side 59 9: 9: 2.3 (i) Substitute y = 23 into the left-hand side of the equation y2 23y 0, and explain why this shows that y 23 is indeed a solution of the equation. (ii) Write out a complete solution of the equation 3;? 23y 0. (iii) Explain, as if directly to the student, why their solution is inadequate. (f) Solve the following equation, checking that your solution is correct: 16 56 63: :33 Solution CD ( it ) sum of Arithmetic sequence = 2 n sater where a = first term 1 = last term m= number of terms Here a = 4 1 = 69 f from (is ? 2 = 14 sfrom (is ? . . fume = 14 5 4 + 69 2 2 Sum = 7x73 sum = 511 required