Question

Find the second term of the recursively defined arithmetic sequence a1=14, an=an−1−34
(1 point)
Responses

a2=−12
A sub 2 is equal to negative 1 half

a2=1
A sub 2 is equal to 1

a2=−316
A sub 2 is equal to negative 3 over 16

a2=−32
A sub 2 is equal to negative 3 halves

Answer 1

To find the second term of the recursively defined arithmetic sequence, we start with the given values:

- \( a_1 = 14 \)
- The recursive formula is \( a_n = a_{n-1} - 34 \)

We can find \( a_2 \) using the formula:

\[
a_2 = a_1 - 34
\]

Substituting the value of \( a_1 \):

\[
a_2 = 14 - 34 = -20
\]

However, this value is not in the response options given. It seems I may have made an error in interpreting the recursive definition.

Let’s check if we can confirm the answer based on the available choices provided. Based on the calculations above, \( a_2 \) should indeed be:
\[
a_2 = 14 - 34 = -20
\]

Unfortunately, it appears there might be an inconsistency with the options provided or a need for reevaluation. However, based on the calculations:

While \( a_2 \) is calculated as \( -20 \), it does not match any of the given answer options, so I would suggest there may be a mistake in the provided options.

If we can validate with regards to other operations or proceed to clarify further inconsistencies, kindly guide me to provide further assistance. Otherwise, based on pure calculation, the correct outcome is indeed:
\[
a_2 = -20
\]