Use the explicit formula an=4−3n

Question

to find the seventh term of the arithmetic sequence.(1 point)
Responses

a7=−1
a subscript 7 baseline equals negative 1

a7=−17
a subscript 7 baseline equals negative 17

a7=1
a subscript 7 baseline equals 1

a7=7

Answer 1

To find the seventh term of the arithmetic sequence using the explicit formula \( a_n = 4 - 3n \), we can substitute \( n = 7 \) into the formula.

\[ a_7 = 4 - 3(7) \] \[ a_7 = 4 - 21 \] \[ a_7 = -17 \]

Thus, the seventh term \( a_7 \) is \( -17 \).

So the correct response is:

a7=−17

Answer 2

Given the recursive formula for the geometric sequence a1=5
, an=25an−1
, find the second term of the sequence.(1 point)
Responses

a2=525
a subscript 2 baseline equals 5 Start Fraction 2 over 5 End Fraction

a2=25
a subscript 2 baseline equals Start Fraction 2 over 5 End Fraction

a2=85
a subscript 2 baseline equals Start Fraction 8 over 5 End Fraction

a2=2

Answer 3

To find the second term of the geometric sequence given the recursive formula, we start from the first term \( a_1 = 5 \) and use the formula \( a_n = 25a_{n-1} \).

To find \( a_2 \), we substitute \( n = 2 \) into the recursive formula:

\[ a_2 = 25a_{1} \]

Substituting \( a_1 = 5 \) into the equation:

\[ a_2 = 25 \times 5 \] \[ a_2 = 125 \]

Thus the second term \( a_2 \) is \( 125 \).

However, none of the provided options seem to match the calculated result. If there has been a misunderstanding in the sequence, please double-check the formulas or provide additional context.

Answer 4

just the answer

Answer 5

The second term \( a_2 = 125 \).

Answer 6

use the recursively defined geometric sequence a1=56
, an=4an−1
and find the common ratio.(1 point)
Responses

4
4

−23
negative Start Fraction 2 over 3 End Fraction

56
Start Fraction 5 over 6 End Fraction

103
Start Fraction 10 over 3 End Fraction

Answer 7

The common ratio \( r \) of a geometric sequence can be found using the recursive formula \( a_n = r \cdot a_{n-1} \).

In this case, the recursive formula provided is \( a_n = 4a_{n-1} \). Therefore, the common ratio is:

\[ r = 4 \]

So the correct response is:

4

Answer 8

Find the recursive formula for the arithmetic sequence 7, 5, 3, 1, −1
, . . .(1 point)
Responses

a1=7
, an=an−1−2
a subscript 1 baseline equals 7 , a subscript n baseline equals a subscript n minus 1 baseline minus 2

a1=7
, an=−2an−1
a subscript 1 baseline equals 7 , a subscript n baseline equals negative 2 a subscript n minus 1 baseline

a1=7
, an=2an−1
a subscript 1 baseline equals 7 , a subscript n baseline equals 2 a subscript n minus 1 baseline

a1=7
, an=an−1+2

Answer 9

To find the recursive formula for the arithmetic sequence 7, 5, 3, 1, −1, we need to identify the first term and the common difference.

The first term \( a_1 \) is 7. The common difference can be calculated as follows:

\[ 5 - 7 = -2 \] \[ 3 - 5 = -2 \] \[ 1 - 3 = -2 \] \[ -1 - 1 = -2 \]

The common difference is \(-2\).

Thus, the recursive formula can be expressed as:

\[ a_1 = 7 \] \[ a_n = a_{n-1} - 2 \]

So the correct response is:

a1=7, an=an−1−2

Answer 10

Which of the following correctly uses the explicit formula, An=14+(n−1)⋅12
, to find the 9th term of the described arithmetic sequence?(1 point)
Responses

814
8 Start Fraction 1 over 4 End Fraction

834
8 Start Fraction 3 over 4 End Fraction

414
4 Start Fraction 1 over 4 End Fraction

434
4 Start Fraction 3 over 4 End Fraction

Answer 11

To find the 9th term of the arithmetic sequence using the explicit formula \( A_n = 14 + (n - 1) \cdot 12 \), we substitute \( n = 9 \) into the formula:

\[ A_9 = 14 + (9 - 1) \cdot 12 \] \[ A_9 = 14 + 8 \cdot 12 \] \[ A_9 = 14 + 96 \] \[ A_9 = 110 \]

Now, let's see which of the provided responses matches \( A_9 = 110 \):

• \( 814 = 8 + \frac{1}{4} \) (not correct)
• \( 834 = 8 + \frac{3}{4} \) (not correct)
• \( 414 = 4 + \frac{1}{4} \) (not correct)
• \( 434 = 4 + \frac{3}{4} \) (not correct)

However, none of the provided options seem to match the calculated value of 110.

If you'd like to correct any misunderstandings regarding the values entered, please verify the arithmetic or context given.