(a) {i} For the nite arithmetic sequence a,s,11,...,44. write down the rst term a, the diEerence {1'1 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} (4:: 33(71- + 9) (ii) [To as)? (c) Factorise 35h? 493:2. (d) {i} Factorise the quadratic expression 1'2 + 3:}: 28. {ii} Use your answer to part [d){i} to solve the quadratic equation a\": + 3:}: 23 = I], 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 the reasoning. 'Tl-seeaua't'lonis: 3163;:{3 Add Is, to each side: 3'"- = '93 Divide each side by 3|: 3= I? {i} Substitute y = 19 into the left-hand side of the equation 3;: 193,- = D, and explain why this shows that y = 19 is indeed a solution of the equation. {ii} Write out a complete solution of the equation 3:2 193,.- = D. {iii} Explain, as if directly to the student1 why their solution is inadequate. (f) Solve the following equation1 checking that your solution is correct: 24 72 91: a+3'