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.
a1=[ ]
d=[ ]
To find the first term, \(a_1\), we can substitute \(n = 1\) into the given function:
\(f(1) = -8(1) + 19 = -8 + 19 = 11\)
So, the first term of the sequence (\(a_1\)) is 11.
Next, to find the common difference, \(d\), we can find the value of the function at \(n = 2\) and subtract the value at \(n = 1\) to get the difference:
\(f(2) = -8(2) + 19 = -16 + 19 = 3\)
Common difference, \(d = f(2) - f(1) = 3 - 11 = -8\)
Therefore, the common difference of the sequence (\(d\)) is -8.