Answer:
The first term is 13/3 and the common difference is d = 1/12
The formula is a(n) = 13/3 + (1/12)(n - 1)
Explanation:
The general equation for an arithmetic progression is:
a(n) = a(1) + d(n - 1), where d is the common difference/
Case 1: n = 7: 29/6 = a(1) + d(7 - 1), or 29/6 = a(1) + d(6)
Case 2: n = 15: 11/2 = a(1) + d(15 - 1) = a(1) + d(14)
Then our system of linear equations is:
a(1) + 6d = 29/6
a(1) + 14d = 11/2
Let's solve this by elimination by addition and subtraction. Subtract the first equation from the second. We get:
Substituting 1/12 for d in the first equation, we get:
a(1) + 14(1/12) = 11/2 or 66/12 (using the LCD 12)
Then a(1) = 66/12 - 14/12 = 52/12 = 13/3
The first term is 13/3 and the common difference is d = 1/12
The arithmetic sequence formula for this problem is thus:
a(n) = 13/3 + (1/12)(n - 1) 8