Question 6 25 marks This question is based on your work on M U123 up to and including Unit 9. (a) (i) For the nite arithmetic sequence 439.14....g. write down the rst term a, the common difference d and the last term L, and hence nd the number of terms it 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) (Ta: :3)(3;1: | 4) (11) [4a 7b)? (c) Factorise 16h.2 49kg. (d) (i) Factorise the quadratic expression $2 6:1: :35. (ii) Use your answer to part (d) (1) to solve the quadratic equation 1:2 6:1: 5-5 : (J, 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 eQua-tion is: 52- - 2.39 = O Add 2.3; to each side: 92- = 2.33 Divide each side 59 9: 3| = 2.3 (1) Substitute y = 23 into the lefthand side of the equation '92 23y : (J, and explain why this shows that y : 23 is indeed a solution of the equation. (ii) Write out a complete solution of the equation 3,12 23y : (J. (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 :36 6 a: m | 3'