Final answer:
To find the first term and the common difference of the arithmetic progression, we use the given 5th and 8th term values and the formula for the nth term of an arithmetic sequence. Solving the resulting equations gives a first term of -10 and a common difference of 4.
Step-by-step explanation:
The student's question relates to finding the first term and the common difference of an arithmetic progression given the 5th and 8th terms. In an arithmetic progression, the nth term can be found using the formula an = a1 + (n - 1)d, where a1 is the first term and d is the common difference.
Given that the 5th term (a5) is 6, we can write:
a5 = a1 + 4d = 6
And the 8th term (a8) is 18:
a8 = a1 + 7d = 18
By subtracting the first equation from the second, we find the common difference d:
18 - 6 = (a1 + 7d) - (a1 + 4d)
12 = 3d
d = 4
Now substituting d back into the first equation gives us the first term a1:
6 = a1 + 4(4)
a1 = -10
Therefore, the first term of the arithmetic progression is -10 and the common difference is 4.