SPM 2024 Add Maths Paper 1, Question 7Progressions

Solved on video in English and Bahasa Melayu · Form 4, Progressions · 5:10 video

The question

(a)(i)

It is given that the first three terms of a sequence are 4, 8, 16. (i) State the type of sequence. Give a reason for your answer.

(a)(ii)

(ii) Hence, find the n^th term of the sequence.

(b)

In an arithmetic progression, the 2nd term is 5p − 10 and the 10th term is 7 times the first term, a. Express a in terms of p.

(c)

A polygon with n sides is drawn such that the sizes of its interior angles form an arithmetic progression. It is given that the size of the largest interior angle is 5 times the size of the smallest interior angle, a. Express a in terms of n.

Part (a)(i)

Step 1

Calculate the ratio of consecutive terms: r₁ = T₂/T₁ = 8/4 = 2; r₂ = T₃/T₂ = 16/8 = 2.

Why this step

In a geometric progression we multiply by the same number each time. Dividing each term by the one before it shows whether that number stays constant.

1 more step, with the reason for it, in the full solution

Final answer

Geometric progression, because the common ratio is constant (2)

Where students lose marks

Watch out: after showing the ratios are equal, you must name the type. Write “geometric progression” in words.

Part (a)(ii)

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

Final answer

T_n = 2^(n+1)

Where students lose marks

Watch out: don't stop at 4(2)^(n−1). Simplify it to 2^(n+1), the simplest form.

Part (b)

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

Final answer

a = 3p − 6

Where students lose marks

Watch out: multiply 9 by every term in the bracket, then collect like terms and divide all of 45p − 90 by 15.

Part (c)

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

Final answer

a = (60n − 120)/n

Where students lose marks

Watch out: the AP sum alone can't give a. You must equate it to the polygon angle sum, (n − 2) × 180°.

Watch every step of this question solved on video (5:10), with the reason behind each step and a box that checks your own answer.

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