Question

Find the second term of the recursively defined arithmetic sequence a1=1/4, an=an−1−3/4
(1 point)
Responses

a2=1
A sub 2 is equal to 1

a2=−1/2
A sub 2 is equal to negative 1 half

a2=−3/2
A sub 2 is equal to negative 3 halves

a2=−3/16

Answer 1

To find the second term \( a_2 \) of the recursively defined arithmetic sequence given by \( a_1 = \frac{1}{4} \) and \( a_n = a_{n-1} - \frac{3}{4} \), we follow these steps:

1. The first term \( a_1 = \frac{1}{4} \).

2. To find the second term \( a_2 \), we use the recursive formula:
\[
a_2 = a_1 - \frac{3}{4}
\]

3. Plugging in the value of \( a_1 \):
\[
a_2 = \frac{1}{4} - \frac{3}{4}
\]

4. This simplifies to:
\[
a_2 = \frac{1 - 3}{4} = \frac{-2}{4} = -\frac{1}{2}
\]

Thus, the second term \( a_2 \) of the sequence is \(-\frac{1}{2}\).

The correct response is:
**a2=−1/2**