Sources: Visual - various maths sites (credits to original creator) Questions - Dong Zong's Textbook suitable for SUEC (Maths), SPM (Maths and Add Maths) too

3. 𝒑𝒈 𝟏𝟐𝟔

5. 𝒑𝒈 𝟏𝟐𝟒

6. 𝒑𝒈 𝟏𝟐𝟒

7. 𝒑𝒈 𝟏𝟐𝟔

8. 𝒑𝒈 𝟏𝟐𝟓

9. 𝒑𝒈 𝟏𝟐𝟔

10. 𝒑𝒈 𝟏𝟐𝟔

11. 𝒑𝒈 𝟏𝟐𝟔
𝑏2
= 𝑎𝑐
𝑏2 𝑛
= 𝑎𝑐 𝑛
∴ 𝑎𝑛, 𝑏𝑛, 𝑐𝑛 𝑖𝑠 𝐺𝑃
𝑇𝑝 = 𝐴𝑅𝑝−1 = 𝑎
𝑇𝑞 = 𝐴𝑅𝑞−1 = 𝑏
𝑇𝑟 = 𝐴𝑅𝑟−1 = 𝑐
𝑎 𝑞 − 𝑟𝑏 𝑟 − 𝑝𝑐 𝑝 − 𝑞
= 𝐴𝑅𝑝−1 𝑞 − 𝑟
𝐴𝑅𝑞−1 𝑟 − 𝑝
𝐴𝑅𝑟−1 𝑝 − 𝑞
= 𝐴 𝑞 − 𝑟 + 𝑟 −𝑝 + 𝑝−𝑞
𝑅(𝑝−1)(𝑞−𝑟)+(𝑞−1)(𝑟−𝑝)+(𝑟−1)(𝑝−𝑞)
= 𝐴 0 𝑅𝑝𝑞−𝑝𝑟−𝑞+𝑟 +𝑞𝑟−𝑝𝑞−𝑟−𝑝 +𝑟𝑝−𝑟𝑞+𝑞
= 𝐴 0
𝑅0
= 1

12. 𝒑𝒈 𝟏𝟐𝟕

13. 𝒑𝒈 𝟏𝟐𝟖

14. 𝒑𝒈 𝟏𝟐𝟖

15. 𝒑𝒈 𝟏𝟐𝟖 − 𝟏𝟐𝟗

16. 𝒑𝒈 𝟏𝟐𝟗
𝑆6 = 9𝑆3
𝑎 1 − 𝑟6
1 − 𝑟
=
9𝑎 1 − 𝑟3
1 − 𝑟
1 − 𝑟6
= 9 1 − 𝑟3
= 9 − 9𝑟3
𝑟6 − 9𝑟3 + 8 = 0
(𝑟3
−8)(𝑟3
− 1) = 0
𝑟 = 2 𝑜𝑟 𝑟 = 1 (𝑖𝑛𝑣𝑎𝑙𝑖𝑑)

17. 𝒑𝒈 𝟏𝟐𝟖
2𝑛𝑑 𝑌𝑒𝑎𝑟 𝑆𝑎𝑙𝑒𝑠
3𝑟𝑑 𝑌𝑒𝑎𝑟 𝑆𝑎𝑙𝑒𝑠

18. 𝒑𝒈 𝟏𝟐𝟗

19. 𝒑𝒈 𝟏𝟐𝟗

20. 𝒑𝒈 𝟏𝟑𝟎

21. 𝒑𝒈 𝟏𝟑𝟎

22. 𝒑𝒈 𝟏𝟑𝟎

23. 𝒑𝒈 𝟏𝟑𝟏

24. 𝑇3 = 27, 𝑇6 = −8, 𝑆4 = ?
𝑇3 = 𝑎𝑟2 = 27 − − ①
𝑇6 = 𝑎𝑟5
= −8 − − ②
② ÷ ① 𝑟 3 =
− 2
3
3
𝑟 = −
2
3
𝑎 =
243
4
𝑆4 =
117
4