To find \( a_7 \) in the sequence 19, 15, 11, 7, 3, we first observe the pattern in the sequence.
The first five terms are as follows:
- \( a_1 = 19 \)
- \( a_2 = 15 \)
- \( a_3 = 11 \)
- \( a_4 = 7 \)
- \( a_5 = 3 \)
To identify the pattern, we can determine the common difference:
- \( 15 - 19 = -4 \)
- \( 11 - 15 = -4 \)
- \( 7 - 11 = -4 \)
- \( 3 - 7 = -4 \)
Thus, the sequence is an arithmetic sequence with a common difference of -4.
Now, we can express the \( n \)-th term of the sequence using the formula for an arithmetic sequence:
\[ a_n = a_1 + (n - 1) \cdot d \]
where \( d \) is the common difference. Substituting in the values we have:
\[ a_n = 19 + (n - 1)(-4) \]
Now, we can calculate \( a_7 \):
\[ a_7 = 19 + (7 - 1)(-4) \] \[ a_7 = 19 + 6 \cdot (-4) \] \[ a_7 = 19 - 24 \] \[ a_7 = -5 \]
Thus, the correct response is:
\( a_7 = -5 \)
Thus, the subscript notation for \( a_7 \) is:
a subscript 7 baseline equals negative 5