Calculate upper S subscript 4 for the sequence defined by left-brace a subscript n baseline right-brace equals left-brace 19 minus 4 n right-brace.

Question

(1 point)
Responses

3
3

26
26

36
36

55

Answer 1

To calculate the upper \( S_4 \) for the sequence defined by \( a_n = 19 - 4n \), we first need to determine the first 4 terms of the sequence \( a_n \).

1. Calculate the terms:

   • For \( n = 1 \): \[ a_1 = 19 - 4 \cdot 1 = 19 - 4 = 15 \]

   • For \( n = 2 \): \[ a_2 = 19 - 4 \cdot 2 = 19 - 8 = 11 \]

   • For \( n = 3 \): \[ a_3 = 19 - 4 \cdot 3 = 19 - 12 = 7 \]

   • For \( n = 4 \): \[ a_4 = 19 - 4 \cdot 4 = 19 - 16 = 3 \]

2. Identify the four terms: The first four terms of the sequence are: \[ a_1 = 15, a_2 = 11, a_3 = 7, a_4 = 3 \]

3. Calculate \( S_4 \): \( S_4 \) is defined as the sum of the first 4 terms of the sequence: \[ S_4 = a_1 + a_2 + a_3 + a_4 \] \[ S_4 = 15 + 11 + 7 + 3 \]

   Now, let's calculate it step by step: \[ 15 + 11 = 26 \] \[ 26 + 7 = 33 \] \[ 33 + 3 = 36 \]

Thus, the value of \( S_4 \) is \( 36 \).

Therefore, the correct response is:

36