Problem:Solve the General term of the sequence.
Because of Covid-19 pandemic, a certain church organization was able to solicit 14, 500 kg of rice from kindhearted people. On their first day of distribution, this organization was able to distribute 250 kg, 365 kg on the second day, 480 kg on the third day, and so on. How many kilograms of goods were distributed on the 12th day?
Solution:(Assuming that distribution followed a pattern)
First, to find the answer, you need to:
a. Write the given sequence:
b. Label the terms of the sequence:
- a_1 = 250
- a_2 = 365
- a_3 = 480
c. What is asked?
- The 12th term from the sequence
d. Is the pattern increasing or decreasing? By how much each time?
- Notice that each term increased by 115 each time.
Second, To solve the problem, formulate the general rule:
a. The partial equation is
b. To complete the equation, substitute the values of n = {1, 2, 3} to the partial equation.
- a_n = 115n
- a_1 = 115(1) + c
- a_2 = 115(2) + c
- a_3 = 115(3) + c
Perform the operations and think of a number to be added in replacement to constant (c) to make it equal to the terms of the sequence.
1st term of the sequence:
- a_n = 115n + c
- a_1 = 115(1) + c
- 250 = 115(1) + c
- 250= 115 + c
- c = 250 - 115
- c = 135
2nd term of the sequence:
- a_n = 115n + c
- a_2 = 115(2) + c
- 365 = 115(2) + c
- 365 = 230 + c
- c = 365 - 230
- c = 135
3rd term of the sequence:
- a_n = 115n + c
- a_3 = 115(3) + c
- 480 = 115(3) + c
- 480 = 365 + c
- c = 480 - 365
- c = 135
Therefore, the general term of the sequence is a_n = 115n + 135.
And last, to solve for the 12th term (a_12), let n = 12
- a_n = 115n + 135
- a_12 = 115(12) + 135
- a_12 = 1,380 + 135
- a_12 = 1,515
Answer:∴ Thus, there are 1,515 kilograms of rice distributed on the 12th day.
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