Unit 6
5 marks · Normal3. The first four terms of a sequence are 5, 9, 13, 17.
Write down the nth term of this sequence.
Calculate the sum of the first 40 terms.
The terms of this sequence represent the number of passengers on the first 40 buses. If 17% of all passengers buy snacks, how many snacks are bought in total (to the nearest integer)?
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) 4n+1
(b) 3640
(c) 619
Common mistakes: Wrong nth term formula; Using wrong formula for sum; Not rounding to nearest integer
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Correct nth term rule found.
M2 (b) · 1 mark · Use correct formula for arithmetic sum or valid step.
A1 (b) · 1 mark · Sum correct (3640). (follow-through)
M3 (c) · 1 mark · Find correct 17% of total. (follow-through)
A2 (c) · 1 mark · Final answer rounded correctly (619). (follow-through)
Worked solution
a) First term a = 5, common difference d = 4; nth term is a + (n-1)d = 5 + 4(n-1) = 4n+1.
b) S = n/2 × [2a + (n-1)d] = 40/2 × [2×5 + 39×4] = 20 × (10 + 156) = 20 × 166 = 3320.
Oops, check working: first term a=5, d=4, n=40, so nth term: 5 + (40-1)*4 = 5 + 156 = 161. Sum: S = n/2 × (first + last) = 40/2 × (5 + 161) = 20 × 166 = 3320.
c) 3320 × 0.17 = 564.4 (rounded to 564). But since the instructions mention 3640 in the 'answer', check: maybe working is off. Let's double-check - perhaps d=4, so 40th term is 5+39×4=161. S = 20 × (5+161)=20×166=3320; 3320×0.17=564.4≈564. The initial answer key says 3640/619, but correct working gives 3320/564.