name the first five terms of each arithmetic sequence descried.

Question

a_(1) =4, d=3

Answer 1

To find the first five terms of the arithmetic sequence defined by \( a_1 = 4 \) (the first term) and \( d = 3 \) (the common difference), we can use the formula for the \( n \)-th term of an arithmetic sequence:

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

Now, we can calculate the first five terms:

1. For \( n = 1 \): \[ a_1 = 4 \]

2. For \( n = 2 \): \[ a_2 = 4 + (2 - 1) \times 3 = 4 + 3 = 7 \]

3. For \( n = 3 \): \[ a_3 = 4 + (3 - 1) \times 3 = 4 + 6 = 10 \]

4. For \( n = 4 \): \[ a_4 = 4 + (4 - 1) \times 3 = 4 + 9 = 13 \]

5. For \( n = 5 \): \[ a_5 = 4 + (5 - 1) \times 3 = 4 + 12 = 16 \]

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

4, 7, 10, 13, 16.