An arithmetic sequence is represented by the linear function f(n)=−8n+19. Find the first term, a1, and the common difference, d, of the sequence.
To find the first term, a1, we can plug in n=1 into the function f(n)=−8n+19:
a1 = f(1) = -8(1) + 19 = -8 + 19 = 11
Therefore, the first term of the arithmetic sequence is a1 = 11.
To find the common difference, we can subtract the value of the function at n=1 from the value of the function at n=2 since the difference between consecutive terms in an arithmetic sequence is constant (the common difference):
d = f(2) - f(1) = (-8(2) + 19) - (-8(1) + 19) = -16 + 19 - (-8 + 19) = 3 - 11 = -8
Therefore, the common difference of the arithmetic sequence is d = -8.