Write down in terms of n, an expression for the nth term of the following sequences:
a) 12 10 8 6 4
b) 25 20 15 20 5

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)

75

step-by-step explanation: