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What are the first five terms of the arithmetic sequence defined explicitly by the formula a subscript n baseline equals 14 minus 3 n?

(1 point)
Responses

negative 3, 0, 3, 6, 9
Image with alt text: negative 3 , 0, 3, 6, 9

14, 17, 20, 23, 26
14, 17, 20, 23, 26

14, 11, 8, 5, 2
14, 11, 8, 5, 2

11, 8, 5, 2, negative 1

1 answer

To find the first five terms of the arithmetic sequence defined by the formula \( a_n = 14 - 3n \), we can substitute \( n = 1, 2, 3, 4, \) and \( 5 \) into the formula:

  1. For \( n = 1 \): \[ a_1 = 14 - 3(1) = 14 - 3 = 11 \]

  2. For \( n = 2 \): \[ a_2 = 14 - 3(2) = 14 - 6 = 8 \]

  3. For \( n = 3 \): \[ a_3 = 14 - 3(3) = 14 - 9 = 5 \]

  4. For \( n = 4 \): \[ a_4 = 14 - 3(4) = 14 - 12 = 2 \]

  5. For \( n = 5 \): \[ a_5 = 14 - 3(5) = 14 - 15 = -1 \]

So, the first five terms of the sequence are: 11, 8, 5, 2, -1.

Thus, the correct response is: 11, 8, 5, 2, negative 1.