The complete table of values for the sequence is
Position 1 4 8 13 19 25
Term 12 3 -9 -24 -42 -60
How to complete the table of values for the sequence
From the question, we have the following parameters that can be used in our computation:
The table of values
Where, we have
f(1) = 12
f(25) = -16
The above means that the first term is 12
The nth term is then represented as
f(n) = a + (n - 1) * d
So, we have
f(n) = 12 + (n - 1) * d
Substitute the known values in the above equation, so, we have the following representation
12 + (25 - 1) * d = -60
24d = -72
Evaluate
d = -3
So, we have
f(n) = 12 - 3(n - 1)
f(n) = 15 -3n
Completing the table of values, we have
f(8) = 15 -3 * 8 = -9
f(19) = 15 -3 * 19 = -42
Also, we have
15 - 3n = 3
-3n = -12
n = 4
15 - 3n = -24
-3n = -39
n = 13
So, the table of value is
Position 1 4 8 13 19 25
Term 12 3 -9 -24 -42 -60