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.

Answer 1

To find the first term, a1, of the sequence, we need to find the value of f(1).

Given f(n) = -8n + 19, substituting n = 1, we get:
f(1) = -8(1) + 19
f(1) = -8 + 19
f(1) = 11

Therefore, the first term, a1, of the sequence is 11.

To find the common difference, d, we notice that the formula for the nth term of an arithmetic sequence is:
an = a1 + (n-1)d

Comparing this formula with f(n) = -8n + 19, we can see that a1 = 11 and d = -8 (the coefficient of n).

Therefore, the common difference, d, of the sequence is -8.