`a_n = 3 - 4(n - 2)` Write the first 5 terms of the sequence. Determine whether the dequence is arithmetic. If so, then find the common...

The given formula of nth term of a sequence is:

`a_n = 3-4(n-2)`

To solve for the first five terms of a sequence, plug-in the following values of n to the formula.

For the first term, plug-in n=1.

`a_1=3-4(1-2) = 7`

For the second term, plug-in n=2.

`a_2=3-4(2-2)=3`

For the third term, plug-in n=3.

`a_3=3-4(3-2)=-1`

For the second term, plug-in n=4.

`a_4=3-4(4-2)=-5`

And for the fifth term, plug-in n=5.

`a_5=3-4(5-2)=-9`

Therefore, the first five terms of the sequence are a_n={7, 3, -1, -5, -9,...}.

To determine if it is an arithmetic sequence, subtract a pair of terms. The pair  should be consecutive terms. If there is a common difference, then it is an arithmetic sequence.

`d= a_2-a_1 = 3-7=-4`

`d=a_3-a_2=-1-3=-4`

`d=a_4-a_3=-5-(-1)=-4`

`d=a_5-a_4=-9-(-5)=-4`

Thus, the given `a_n` is an arithmetic sequence and its common difference between consecutive terms is -4.