Question

What is the explicit formula for the nth term in the given arithmetic sequence 16, 19, 22, 25, ...?

A) n + 15
B) 16 + 3n
C) 16n
D) 22n - 3

Answer 1

The explicit formula for the nth term in the given arithmetic sequence 16, 19, 22, 25, ... is 3n + 13.

Step-by-step explanation:

The explicit formula for the nth term in an arithmetic sequence is given by the formula:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, and d is the common difference.

In the given arithmetic sequence 16, 19, 22, 25, ..., the first term (a1) is 16 and the common difference (d) is 3. Substitute these values into the formula to find the explicit formula for the nth term:

an = 16 + (n - 1)3 = 16 + 3n - 3 = 3n + 13

So, the explicit formula for the nth term in the given arithmetic sequence is 3n + 13.