Question

Given the first five terms of the sequence 19, 15, 11, 7, 3... use the subscript notation to describe a7

Answer 1

To describe the 7th term (a7) of the sequence 19, 15, 11, 7, 3, we first need to observe the pattern in the sequence.

The first term, \( a_1 \), is 19.
The second term, \( a_2 \), is 15.
The third term, \( a_3 \), is 11.
The fourth term, \( a_4 \), is 7.
The fifth term, \( a_5 \), is 3.

We can see that each term is decreasing by 4. Therefore, this is an arithmetic sequence with a common difference of -4.

The general formula for the nth term of an arithmetic sequence can be given by:
\[ a_n = a_1 + (n-1) \cdot d \]
where \( a_1 \) is the first term and \( d \) is the common difference.

In this case:
- \( a_1 = 19 \)
- \( d = -4 \)

Now, substituting these values into the formula to find \( a_7 \):

\[
a_7 = a_1 + (7-1) \cdot d
\]
\[
a_7 = 19 + (6) \cdot (-4)
\]
\[
a_7 = 19 - 24
\]
\[
a_7 = -5
\]

So, \( a_7 \) in subscript notation is \( a_7 = -5 \).