Question
Find the first five terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.
a n = 72n − 11
a n = 72n − 11
Answers
GPT-4o mini
To find the first five terms of the sequence defined by the formula \( a_n = 72n - 11 \), we will calculate the value of \( a_n \) for \( n = 1, 2, 3, 4, \) and \( 5 \).
1. For \( n = 1 \):
\[
a_1 = 72(1) - 11 = 72 - 11 = 61
\]
2. For \( n = 2 \):
\[
a_2 = 72(2) - 11 = 144 - 11 = 133
\]
3. For \( n = 3 \):
\[
a_3 = 72(3) - 11 = 216 - 11 = 205
\]
4. For \( n = 4 \):
\[
a_4 = 72(4) - 11 = 288 - 11 = 277
\]
5. For \( n = 5 \):
\[
a_5 = 72(5) - 11 = 360 - 11 = 349
\]
Thus, the first five terms of the sequence are:
\[
61, 133, 205, 277, 349
\]
1. For \( n = 1 \):
\[
a_1 = 72(1) - 11 = 72 - 11 = 61
\]
2. For \( n = 2 \):
\[
a_2 = 72(2) - 11 = 144 - 11 = 133
\]
3. For \( n = 3 \):
\[
a_3 = 72(3) - 11 = 216 - 11 = 205
\]
4. For \( n = 4 \):
\[
a_4 = 72(4) - 11 = 288 - 11 = 277
\]
5. For \( n = 5 \):
\[
a_5 = 72(5) - 11 = 360 - 11 = 349
\]
Thus, the first five terms of the sequence are:
\[
61, 133, 205, 277, 349
\]
Find the first five terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.
a n = 52n + 30
a n = 52n + 30
GPT-4o mini
To find the first five terms of the sequence defined by \( a_n = 52n + 30 \), we will calculate the value of \( a_n \) for \( n = 1, 2, 3, 4, \) and \( 5 \).
1. For \( n = 1 \):
\[
a_1 = 52(1) + 30 = 52 + 30 = 82
\]
2. For \( n = 2 \):
\[
a_2 = 52(2) + 30 = 104 + 30 = 134
\]
3. For \( n = 3 \):
\[
a_3 = 52(3) + 30 = 156 + 30 = 186
\]
4. For \( n = 4 \):
\[
a_4 = 52(4) + 30 = 208 + 30 = 238
\]
5. For \( n = 5 \):
\[
a_5 = 52(5) + 30 = 260 + 30 = 290
\]
Thus, the first five terms of the sequence are:
\[
82, 134, 186, 238, 290
\]
1. For \( n = 1 \):
\[
a_1 = 52(1) + 30 = 52 + 30 = 82
\]
2. For \( n = 2 \):
\[
a_2 = 52(2) + 30 = 104 + 30 = 134
\]
3. For \( n = 3 \):
\[
a_3 = 52(3) + 30 = 156 + 30 = 186
\]
4. For \( n = 4 \):
\[
a_4 = 52(4) + 30 = 208 + 30 = 238
\]
5. For \( n = 5 \):
\[
a_5 = 52(5) + 30 = 260 + 30 = 290
\]
Thus, the first five terms of the sequence are:
\[
82, 134, 186, 238, 290
\]
Find the 40th term of the sequence described below, where n represents the position of a term in the sequence.
a n = n − 29
a n = n − 29
GPT-4o mini
To find the 40th term of the sequence defined by the formula \( a_n = n - 29 \), we will substitute \( n = 40 \) into the equation.
\[
a_{40} = 40 - 29
\]
Calculating this gives:
\[
a_{40} = 11
\]
Therefore, the 40th term of the sequence is **11**.
\[
a_{40} = 40 - 29
\]
Calculating this gives:
\[
a_{40} = 11
\]
Therefore, the 40th term of the sequence is **11**.
Find the 9th term of the sequence described below, where n represents the position of a term in the sequence.
a n = –6n
a n = –6n
GPT-4o mini
To find the 9th term of the sequence defined by the formula \( a_n = -6n \), we will substitute \( n = 9 \) into the equation.
\[
a_9 = -6(9)
\]
Calculating this gives:
\[
a_9 = -54
\]
Therefore, the 9th term of the sequence is **-54**.
\[
a_9 = -6(9)
\]
Calculating this gives:
\[
a_9 = -54
\]
Therefore, the 9th term of the sequence is **-54**.
Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.
4, 5, 6, 7, ...
a n =
GPT-4o mini
The sequence you provided is \( 4, 5, 6, 7, \ldots \). This is an arithmetic sequence where each term increases by 1.
To write an expression \( a_n \) that represents the \( n \)th term, observe that:
- When \( n = 1 \), \( a_1 = 4 \)
- When \( n = 2 \), \( a_2 = 5 \)
- When \( n = 3 \), \( a_3 = 6 \)
- When \( n = 4 \), \( a_4 = 7 \)
Notice that if you start from 3 and add \( n \) to it, you get \( 3 + n \).
Thus, the expression for the \( n \)th term of the sequence can be written as:
\[
a_n = n + 3
\]
So, the final expression is:
\[
a_n = n + 3
\]
To write an expression \( a_n \) that represents the \( n \)th term, observe that:
- When \( n = 1 \), \( a_1 = 4 \)
- When \( n = 2 \), \( a_2 = 5 \)
- When \( n = 3 \), \( a_3 = 6 \)
- When \( n = 4 \), \( a_4 = 7 \)
Notice that if you start from 3 and add \( n \) to it, you get \( 3 + n \).
Thus, the expression for the \( n \)th term of the sequence can be written as:
\[
a_n = n + 3
\]
So, the final expression is:
\[
a_n = n + 3
\]
Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.
3, 6, 9, 12, ...
a n =
3, 6, 9, 12, ...
a n =
GPT-4o mini
The sequence you provided is \( 3, 6, 9, 12, \ldots \). This is an arithmetic sequence where each term increases by 3.
To write an expression \( a_n \) that represents the \( n \)th term, observe the following:
- When \( n = 1 \), \( a_1 = 3 \)
- When \( n = 2 \), \( a_2 = 6 \)
- When \( n = 3 \), \( a_3 = 9 \)
- When \( n = 4 \), \( a_4 = 12 \)
Notice that the \( n \)th term can be calculated as \( 3n \).
Thus, the expression for the \( n \)th term of the sequence can be written as:
\[
a_n = 3n
\]
So, the final expression is:
\[
a_n = 3n
\]
To write an expression \( a_n \) that represents the \( n \)th term, observe the following:
- When \( n = 1 \), \( a_1 = 3 \)
- When \( n = 2 \), \( a_2 = 6 \)
- When \( n = 3 \), \( a_3 = 9 \)
- When \( n = 4 \), \( a_4 = 12 \)
Notice that the \( n \)th term can be calculated as \( 3n \).
Thus, the expression for the \( n \)th term of the sequence can be written as:
\[
a_n = 3n
\]
So, the final expression is:
\[
a_n = 3n
\]