Question

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.
(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**