Question

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

a7=−5
a subscript 7 baseline equals negative 5

a7=−4
a subscript 7 baseline equals negative 4

a7=−9
a subscript 7 baseline equals negative 9

a7=−1

Answer 1

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**