(a) (i) For the finite arithmetic sequence 5, 8, 11,..., 44. write down the first term a, the difference d, and the last term L, and hence find 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 find the sum of the arithmetic sequence in part (a)(i). (b) Expand the brackets in the following expressions. (i) (4x-8)(7x+9) (ii) (7a-5b)² (c) Factorise 36h²-49k2.
(a) (i) For the finite arithmetic sequence 5, 8, 11,..., 44. write down the first term a, the difference d, and the last term L, and hence find 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 find the sum of the arithmetic sequence in part (a)(i). (b) Expand the brackets in the following expressions. (i) (4x-8)(7x+9) (ii) (7a-5b)² (c) Factorise 36h²-49k2.
Chapter12: Sequences, Series And Binomial Theorem
Section: Chapter Questions
Problem 327PT: Find the twenty-third term of an arithmetic sequence whose seventh term is 11 and common difference...
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Question
Transcribed Image Text:(a) (i) For the finite arithmetic sequence
5, 8, 11,..., 44.
write down the first term a, the difference d, and the last term L,
and hence find 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 find the
sum of the arithmetic sequence in part (a)(i).
(b) Expand the brackets in the following expressions.
(i) (4x-8)(7x + 9)
(ii) (7a-5b)²
(c) Factorise 36h² - 49k².
(d) (i) Factorise the quadratic expression x² + 3x - 28.
(ii) Use your answer to part (d) (i) to solve the quadratic equation
x² + 3x-28 = 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 the reasoning.
The equation is:
Add 19y to each side:
y²-19y=0
y² = 19y
y = 19
Divide each side By y:
(i) Substitute y = 19 into the left-hand side of the equation
y²-19y = 0, and explain why this shows that y = 19 is indeed a
solution of the equation.
(ii) Write out a complete solution of the equation y2 - 19y = 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:
24
72
<-x
x+3'
9
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