Final answer:
To find the explicit formula for the arithmetic sequence, we need to find the common difference (d) by solving the given equations. Then, we can use the formula for the nth term of an arithmetic sequence to find the explicit formula.
Step-by-step explanation:
To find the explicit formula for the arithmetic sequence, we need to find the common difference (d). Let's use the given information:
- 8th term = 25
- 14th term = 43
We can use the formula for the nth term of an arithmetic sequence:
nth term = a + (n - 1)d, where a is the first term and d is the common difference.
For the 8th term, we have: 25 = a + (8 - 1)d
For the 14th term, we have: 43 = a + (14 - 1)d
Solving these two equations simultaneously will give us the values of a and d, which we can use to form the explicit formula.