Question

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) and the common difference (d) of the arithmetic sequence represented by the linear function f(n) = -8n + 19, we need to understand that in an arithmetic sequence, each term is obtained by adding a constant value (common difference) to the previous term.

The formula for the nth term of an arithmetic sequence is: an = a1 + (n-1)d

Based on the given function f(n) = -8n + 19, we can see that the constant term in the linear function is 19. So, 19 is the first term of the arithmetic sequence, which means a1 = 19.

Next, the coefficient of 'n' in the linear function (-8n) indicates the common difference between consecutive terms. Therefore, the common difference, d, is -8.

So, the first term (a1) of the arithmetic sequence is 19, and the common difference (d) is -8.