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, we need to find the value of f(1):
f(1) = -8(1) + 19
f(1) = -8 + 19
f(1) = 11
Therefore, the first term, a1, of the arithmetic sequence is 11.
To find the common difference, we need to find the difference between two consecutive terms in the sequence. Let's find f(2) and calculate the difference:
f(2) = -8(2) + 19
f(2) = -16 + 19
f(2) = 3
The common difference, d, is the difference between any two consecutive terms in an arithmetic sequence. Therefore, d = f(2) - f(1):
d = 3 - 11
d = -8
Hence, the common difference, d, of the arithmetic sequence is -8.
Apologies for the confusion earlier. The first term, a1, of the arithmetic sequence is the same as f(1), which we already calculated as 11.
Therefore, the first term a1 of the sequence is 11.