To find \( a_7 \) of the sequence given by the terms 19, 15, 11, 7, 3, we first need to identify the pattern.
Looking at the sequence:
- The first term \( a_1 = 19 \)
- The second term \( a_2 = 15 \)
- The third term \( a_3 = 11 \)
- The fourth term \( a_4 = 7 \)
- The fifth term \( a_5 = 3 \)
We can see that each term decreases by 4:
- \( a_2 - a_1 = 15 - 19 = -4 \)
- \( a_3 - a_2 = 11 - 15 = -4 \)
- \( a_4 - a_3 = 7 - 11 = -4 \)
- \( a_5 - a_4 = 3 - 7 = -4 \)
Thus, this is an arithmetic sequence where the first term \( a_1 = 19 \) and the common difference \( d = -4 \).
The general term \( a_n \) of an arithmetic sequence can be expressed as: \[ a_n = a_1 + (n-1) \cdot d \]
Substituting in our values: \[ a_n = 19 + (n-1)(-4) \] \[ a_n = 19 - 4(n-1) \]
Now, let's find \( a_7 \): \[ a_7 = 19 - 4(7-1) \] \[ a_7 = 19 - 4(6) \] \[ a_7 = 19 - 24 \] \[ a_7 = -5 \]
Thus, the correct response is: \[ \text{a}_7 = -5 \]
So, the answer is: a7=−5