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
In an arithmetic sequence, the formula for finding any term in the sequence is given by:
An = a1 + (n-1)d
Where:
An = the nth term
a1 = the first term
n = the position of the term in the sequence
d = the common difference
We are given that the linear function representing the arithmetic sequence is f(n) = -8n + 19. This means that the first term is represented by f(1):
a1 = f(1) = -8(1) + 19 = 11
So, the first term a1 is 11.
We can also find the common difference by finding the difference between any two consecutive terms. Let's find the first two terms:
a1 = 11
a2 = -8(2) + 19 = 3
Now we can find the common difference:
d = a2 - a1 = 3 - 11 = -8
So, the common difference d is -8.