What are the next three terms in the arithmetic sequence −8.4,−7.2,−6.0, . . . ?
The common difference between each term is 1.2.
Therefore, the next three terms in the sequence are:
-4.8, -3.6, -2.4
Actually lemme just use my brain some more
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 nth term is given by the formula:
An = a1 + (n-1)d
where:
An = nth term
a1 = first term
d = common difference
n = term number
Given that the linear function represents the arithmetic sequence, we have:
f(n) = -8n + 19
This is equivalent to the formula for the nth term:
-8n + 19 = a1 + (n-1)d
Comparing coefficients, we see that:
a1 = 19 (the constant term)
d = -8 (the coefficient of n)
Therefore, the first term is a1 = 19 and the common difference is d = -8.