MRSM Trial 2025 Add Maths Paper 1, Question 8Progressions

Solved on video in English · Form 4, Progressions · 5:43 video

The question

(a)

Firdaus joins a 1000-page reading program organized by a library. He reads (6 + x) pages on the first day, (4x − 4) pages on the second day and (7x − 14) pages on the third day.

(a) Determine the type of progression involved. Justify your answer. [Listing out all terms of the sequence is not accepted.]

(b)

Firdaus reads (6 + x) pages on day 1, (4x − 4) on day 2 and (7x − 14) on day 3 of a reading program.

(b) If Firdaus reads 10 pages on the first day, how many pages are read by him on the 14th day?

(c)

The organiser allocates a duration of 4 weeks for the participants to complete the reading (of 1000 pages). With a = 10 and d = 2, prove with calculations whether Firdaus manages to complete his reading within the given period.

MRSM Trial 2025 Add Maths Paper 1, Question 8: the question as drawn in Eduly's video5:43

Part (a)

Step 1

Test the differences between consecutive terms using d = Tₙ − Tₙ₋₁.

Why this step

Just listing the terms isn't accepted. An AP means a constant gap, so we must show the gaps between consecutive terms are equal.

3 more steps, each with the reason for it, in the full solution

Final answer

Arithmetic progression, since T₂ − T₁ = T₃ − T₂ = 3x − 10

Where students lose marks

Watch out: listing terms isn't accepted. Work out both differences, then state clearly that they are equal.

Part (b)

4 more steps, each with the reason for it, in the full solution

Final answer

36 pages

Where students lose marks

Watch out: find x = 4 first to get d = 2, and use (n − 1)d = 13d, not 14d.

Part (c)

5 more steps, each with the reason for it, in the full solution

Final answer

Yes: S₂₈ = 1036 > 1000, so he finishes within 4 weeks

Where students lose marks

Watch out: 4 weeks is 28 days, not 4 or 20. End by comparing 1036 with 1000 and stating your conclusion.

Watch every step of this question solved on video (5:43), with the reason behind each step and a box that checks your own answer.

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