Question 6 - 25 marks This question is based on your work on MU123 up to and including Unit 9. (a) (i) For the finite arithmetic sequence 7, 11, 15, ..., 59. write down the first term a, the common difference d, and the last term L, and hence find the number of terms a of the sequence. Check that your answer is correct. [3] (ii) Use an appropriate formula from Unit 9, Subsection 1.1 to find the sum of the arithmetic sequence in part (a) (i)- [2] (b) Expand the brackets in the following expressions. (i) (5x - 9)(4x + 3) 1-1 (ii) (5a - 96)- (c) Factorise 25h- - 64k-. 191 (d) (i) Factorise the quadratic expression :' + 73 -60. (ii) Use your answer to part (d)(i) to solve the quadratic equation I'+ 7x -60 =0, showing each step in your reasoning. Check that your solution is correct. [2] (e) A student writes down the following piece of work, which contains an error in the reasoning. The equation is: 42 - 314 = 0 Add siy to each side: y = 31y Divide each side by y: H = 31 (i) Substitute y =31 into the left-hand side of the equation y' - 3ly =0. and explain why this shows that y = 31 is indeed a solution of the equation. [2] (ii) Write out a complete solution of the equation y' - 3ly = 0. [2] (iii) Explain, as if directly to the student, why their solution is inadequate. [1] (f) Solve the following equation, checking that your solution is correct: 12 60 [5] 8-I + + 10 Question 7 - 5 marks A score out of 5 marks for good mathematical communication over the entire TMA will be recorded under Question 7. [5]