Answer:
f(n) = 155 - 14(n-1) [Question 1, Arithmetic sequence]
f(15) = -41 [Question 2, 15th term]
Step-by-step explanation:
Given the explicit formula for an arithmetic sequence: f(n) = f(1) + d(n-1).
Where d is the common difference, f(n) is the nth term, and f(1) is the first term.
Given that the first term f(1) is 155 from the table since 1 is n, and 155 is f(n). And the second term f(2) is 141 since n is 2, and 141 is under f(n) on the table when n is 2.
Subtract the two terms to find the common difference: d = f(2) - f(1) = f(3) - f(2) = f(4) - f(3) = ...
d is 155-141= -14.
Remember how the first term in the sequence is 155, and how d is -14, we can make this into an equation:
f(n) = f(1) + d(n-1) → f(n) = 155 - 14(n-1).
We can test this by matching the equation by input, and output to the table:
f(1) = 155 - 14(1-1) = 155
f(2) = 155 - 14(2-1) = 155 - 14 = 141
f(3) = 155 - 14(3-1) = 155 - 28 = 127
f(4) = 155 - 14(4-1) = 155 - 42 = 113
f(5) = 155 - 14(5-1) = 155 - 56 = 99
......
f(15) = 155 - 14(15-1) = 155 - 196 = -41
