4. An environmentalist monitored the water quality of a river in city X by measuring the conductivity of the river monthly. The conductivity of a water body is an early indicator of the water quality. Owing to implementation of activities which were harmful to the nature such as an oil spill, the conductivity in uS/cm of the river decreased. However, a continuous cleaning up plan had been carried out for the river from January until April 2020 and the conductivity measurement for the months had improved as follows: ai. 22. a3. 04. as..., an 3. 12, 27, 48, 75. an a. Let an represents the conductivity for n months since January 2020. By using n in the formula, determine the formula to represent the conductivity sequence, an- [3 marks] b. What is the estimated conductivity for January 2021? [2 marks] c. By assuming bn-1 = an - An-1, the monthly improvement of conductivity can be represented by the following sequence. Based on the given sequence, determine bn. bi, b2, 63, 64, ..., bn = (12-3). (27-12) (48-27). (75-48)....., bn = 9.15. 21. 27...... bn 1 [4 marks] d. Based on the answer from 4(c) and assume m as the upper limit, express the summation of conductivity of improvement in terms of n. [2 marks] e. Based on the answer from 4(d), calculate the summation of conductivity for the first 8 months. [4 marks] 4. An environmentalist monitored the water quality of a river in city X by measuring the conductivity of the river monthly. The conductivity of a water body is an early indicator of the water quality. Owing to implementation of activities which were harmful to the nature such as an oil spill, the conductivity in uS/cm of the river decreased. However, a continuous cleaning up plan had been carried out for the river from January until April 2020 and the conductivity measurement for the months had improved as follows: ai. 22. a3. 04. as..., an 3. 12, 27, 48, 75. an a. Let an represents the conductivity for n months since January 2020. By using n in the formula, determine the formula to represent the conductivity sequence, an- [3 marks] b. What is the estimated conductivity for January 2021? [2 marks] c. By assuming bn-1 = an - An-1, the monthly improvement of conductivity can be represented by the following sequence. Based on the given sequence, determine bn. bi, b2, 63, 64, ..., bn = (12-3). (27-12) (48-27). (75-48)....., bn = 9.15. 21. 27...... bn 1 [4 marks] d. Based on the answer from 4(c) and assume m as the upper limit, express the summation of conductivity of improvement in terms of n. [2 marks] e. Based on the answer from 4(d), calculate the summation of conductivity for the first 8 months. [4 marks]