Question

Given the second term and the common difference of an arithmetic sequence, find the explicit formula

a=8,d=-4
a) aₙ = 8 - 4n
b) aₙ = 8 - 4(n-1)
c) aₙ = 8 - 4(n+1)
d) aₙ = 8 - 4n

Answer 1

The explicit formula for the arithmetic sequence is aₙ = 8 - 4(n - 1).

Step-by-step explanation:

The explicit formula for an arithmetic sequence is given by:

aₙ = a + (n - 1)d

where:

1. aₙ represents the nth term of the sequence
2. a is the second term of the sequence, which is 8 in this case
3. d is the common difference of the sequence, which is -4 in this case
4. n represents the position of the term in the sequence

Substituting the given values into the formula, we have:

aₙ = 8 + (n - 1)(-4)

Therefore, the correct explicit formula for this arithmetic sequence is aₙ = 8 - 4(n - 1) (option b).