Question 6 25 marks This question is based on your work on MU123 up to and including Unit 9. (a) Consider the finite arithmetic sequence: 6, 11, 16, . .. . 61. (i) Write down the first term a, the common difference d, and the last term L, and hence find the number of terms n 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) (7x - 8)(5: + 4) [2] (ii) (4a - 76)2 [2] (c) Factorise 912 - 49k2. [2] (d) (i) Factorise the quadratic expression 2' + 5: - 66. [2] (ii) Use your answer to part (d) (i) to solve the quadratic equation 12 + 5x -66 =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 y - 224 = 0 Add 22y to each side y = 224 Divide each side by y y = 22 (i) Substitute y = 22 into the left-hand side of the equation y' - 22y =0, and explain why this shows that y = 22 is indeed a solution of the equation. (2] (ii) Write out a complete solution of the equation y' - 22y = 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: 5 10- I I+4 [5]