Answer:
a) aₙ = 12 + (n - 1)*(-2)
b) aₙ = 25 + (n - 1)*(-5)
Step-by-step explanation:
These are arithmetic sequeces.
Usually, the n-th term of an arithmetic sequence can be written as
aₙ = aₙ₋₁ + d
or
aₙ = a₁ + (n - 1)*d
where d is the difference between any two consecutive terms.
a) we have the sequence:
12 10 8 6 4
First, we can take the difference between any two consecutive terms to find the value of d (we should check with different pairs, and see if the value of d is always the same):
d = 10 - 12 = -2
d = 8 - 10 = -2
etc.
And the term a₁ is the first term of the sequence, in this case is 12.
Then the n-th term of this sequence can be written as:
aₙ = 12 + (n - 1)*(-2)
b) 25 20 15 20 5
Same as before, first we find the value of d:
d = 20 - 25 = -5
d = 15 - 20 = -5
etc...
We can see that d is equal to -5
and in this case, the first term is 25, then a₁ = 25
Then the n-th term is:
aₙ = 25 + (n - 1)*(-5)
