name the first five terms of each arithmetic sequence descried.

Question

a_(1) =3 d=-1

Answer 1

To find the first five terms of the arithmetic sequence with the first term \( a_1 = 3 \) and common difference \( d = -1 \), we can use the formula for the \( n \)-th term of an arithmetic sequence:

\[ a_n = a_1 + (n-1) \cdot d \]

Now, we can calculate the first five terms:

1. First term \( (a_1) \): \[ a_1 = 3 \]

2. Second term \( (a_2) \): \[ a_2 = a_1 + d = 3 + (-1) = 2 \]

3. Third term \( (a_3) \): \[ a_3 = a_2 + d = 2 + (-1) = 1 \]

4. Fourth term \( (a_4) \): \[ a_4 = a_3 + d = 1 + (-1) = 0 \]

5. Fifth term \( (a_5) \): \[ a_5 = a_4 + d = 0 + (-1) = -1 \]

So, the first five terms of the arithmetic sequence are:

3, 2, 1, 0, -1.