Given the sequence of numbers;
7, 10, 13, 16, 19
The sequence is an arithmetic sequence because it has a common difference of 3.
We are to find the nth term of the arithmetic sequence. The nth term is expressed according to the formula;
Tn = a + (n-1)d
a is the first term
n is the number of terms
d is the common difference
From the sequence;
a = 7
d = 10-7 = 13-10 = 16 - 13 = 3
d = 3
Substitute the given values into the formula;
Tn = a + (n-1)d
Tn = 7 + (n-1) (3)
Tn = 7 + 3n - 3
Tn = 3n + 7 - 3
Tn = 3n + 4
Tn = 4 + 3n
Hence the required function is f(n) = 4 + 3n. Option D is CORRECT.