SPM 2021 Add Maths Paper 1, Question 3Progressions

Solved on video in English and Bahasa Melayu · Form 4, Progressions · 7:19 video

The question

(a)

In a geometric progression, the first term is 217 and the common ratio is 2/3. Find the maximum value of n such that the sum of the first n terms of the progression is less than 650.

(b)

In the same geometric progression (first term 217, common ratio 2/3), find the difference between the 5th term and the sum of all the terms of the progression.

SPM 2021 Add Maths Paper 1, Question 3: the question as drawn in Eduly's video7:19

Part (a)

Step 1

Sum of the first n terms: S_n = a(1 − r^n)/(1 − r), with a = 217 and r = 2/3.

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

Final answer

n = 15

Where students lose marks

Watch out: keep brackets around (2/3)^n, and reverse the inequality sign when you divide by the negative log₁₀(2/3).

Part (b)

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

Final answer

49259/81 = 608 11/81

Where students lose marks

Watch out: 'the sum of all the terms' means the sum to infinity S∞, not S₁₅ or the sum of a few terms.

Watch every step of this question solved on video (7:19), with the reason behind each step and a box that checks your own answer.

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