SPM 2022 Add Maths Paper 2, Question 4Progressions

Solved on video in English and Bahasa Melayu · 3 marks · Form 4, Progressions · 5:36 video

The question

(a)

In a geometric progression, the sum of the first four terms is 16 times the sum of the next four terms.

(a) Show that the common ratio, r, of the progression is 1/2.

[3 marks]

(b)

Using the geometric progression with common ratio r = 1/2:

(b) Given that the difference between the 4th term and the 8th term of the progression is 120, find (i) the first term of the progression, (ii) the sum to infinity of the progression.

SPM 2022 Add Maths Paper 2, Question 4: the question as drawn in Eduly's video5:36

Part (a)

Step 1

Let the first term be a and the common ratio be r. The sum of the first four terms is S₄ and the sum of the next four terms is S₈ − S₄.

Why this step

The next four terms are terms 5 to 8. The first 8 terms minus the first 4 leaves exactly those four terms.

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

Final answer

r = 1/2 (shown)

Where students lose marks

Watch out: after writing S₄ = 16(S₈ − S₄), keep the brackets and simplify carefully. Sign slips give wrong results like r⁴ = −1/15.

Part (b)

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

Final answer

a = 1024, S∞ = 2048

Where students lose marks

Watch out: use a/(1 − r), not a/(r − 1), for the sum to infinity. A negative answer means the two are swapped.

Watch every step of this question solved on video (5:36), with the reason behind each step and a box that checks your own answer.

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