Unit 6
4 marks · Normal8. The sequence {T_n} has nth term T_n = 2n - 1, for n = 1, 2, 3, …
Let A = {T_n | n ∈ N, n ≤ 6}.
List all elements of set A.
Find the sum of all elements of A.
Let S be the set of all odd numbers less than 12. Express S using set-builder notation.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) {1, 3, 5, 7, 9, 11}
(b) 36
(c) S = {x ∈ N | x is odd, 1 ≤ x < 12}
Common mistakes: Forgetting to list correct elements; Calculation errors in sum
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · Lists all 6 correct terms.
M1 (b) · 1 mark · Adds terms or uses correct sum formula.
A1 (b) · 1 mark · Sum = 36. (follow-through)
B2 (c) · 1 mark · Correct set-builder notation.
Worked solution
a) Plug in n=1 to 6: 1,3,5,7,9,11.
b) 1+3+5+7+9+11=36.
c) S = {x ∈ N | x = 2k - 1, 1 ≤ x < 12 } or S = {x ∈ N | x odd, 1 ≤ x < 12}.