`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 difference. (Assume thatn begins with 1)

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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.


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


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


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


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`




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

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