to find the seventh term of the arithmetic sequence.(1 point)
Responses
a7=−17
a subscript 7 baseline equals negative 17
a7=−1
a subscript 7 baseline equals negative 1
a7=1
a subscript 7 baseline equals 1
a7=7
9 answers
To find the seventh term of the sequence given by the explicit formula \( a_n = 4 - 3n \), we need to substitute \( n = 7 \) into the formula.
\[ a_7 = 4 - 3(7) \] \[ a_7 = 4 - 21 \] \[ a_7 = -17 \]
So the seventh term \( a_7 \) is \(-17\).
The correct answer is: a7=−17
To find the second term of the geometric sequence given the recursive formula \( a_1 = 5 \) and \( a_n = \frac{2}{5} a_{n-1} \), we will calculate \( a_2 \) using the formula.
Since we know the first term is \( a_1 = 5 \), we can use it to find \( a_2 \):
\[ a_2 = \frac{2}{5} a_1 = \frac{2}{5} \times 5 \] \[ a_2 = 2 \]
Thus, the second term \( a_2 \) is \( 2 \).
The correct answer is: a2=2
In a geometric sequence, the common ratio \( r \) is the factor by which each term is multiplied to get the next term. Given the recursive formula for the geometric sequence:
The common ratio can be identified from the formula, where \( a_n \) is determined by multiplying the previous term \( a_{n-1} \) by 4.
Therefore, the common ratio \( r \) is:
\[ r = 4 \]
The correct answer is: 4
To find the recursive formula for the arithmetic sequence \( 7, 5, 3, 1, -1, \ldots \), we first identify the first term and the common difference.
Thus, the common difference \( d \) is \( -2 \).
The recursive formula for an arithmetic sequence is given by:
\[ a_n = a_{n-1} + d \]
For our sequence, it becomes:
\[ a_n = a_{n-1} - 2 \]
So, the complete recursive formula for this sequence is:
\[ a_1 = 7, \quad a_n = a_{n-1} - 2 \]
The correct answer is: a1=7, an=an−1−2
To find the 9th term of the arithmetic sequence described by the explicit formula
\[ A_n = \frac{1}{4} + (n - 1) \cdot 12, \]
we need to substitute \( n = 9 \) into the formula.
\[ A_9 = \frac{1}{4} + (9 - 1) \cdot 12 \] \[ A_9 = \frac{1}{4} + 8 \cdot 12 \] \[ A_9 = \frac{1}{4} + 96 \]
Now, we can convert \( 96 \) to a fraction with a common denominator of 4 to combine the terms:
\[ 96 = \frac{96 \cdot 4}{4} = \frac{384}{4}, \]
So,
\[ A_9 = \frac{1}{4} + \frac{384}{4} = \frac{1 + 384}{4} = \frac{385}{4}. \]
Now, let's convert \(\frac{385}{4}\) back to a mixed number if useful:
\[\frac{385}{4} = 96.25 = 96\frac{1}{4}.\]
Let's check the available responses for \( \frac{385}{4} \):
It appears there has been an error in interpreting the choices or in the calculations. On just confirming our computed term:
\[ A_9 = \frac{385}{4}. \]
This value suggests \( 96\frac{1}{4} \) which is not listed; rather \( \frac{381}{4} \) or any fraction close to mixed from available choices may have been misplaced.
Please restate the responses provided. Are any corrections filed on the selections?
