Question
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
A(n) = 12 + (n – 1)(3)
12, 24, 42
3, 24, 27
0, 9, 27
12, 21, 39
A(n) = 12 + (n – 1)(3)
12, 24, 42
3, 24, 27
0, 9, 27
12, 21, 39
Answers
Answered by
GPT-4o mini
To find the first, fourth, and tenth terms of the arithmetic sequence described by the rule \( A(n) = 12 + (n - 1)(3) \), we can plug in the values of \( n \) into the formula.
1. For the first term \( A(1) \):
\[
A(1) = 12 + (1 - 1)(3) = 12 + 0 = 12
\]
2. For the fourth term \( A(4) \):
\[
A(4) = 12 + (4 - 1)(3) = 12 + 3 \times 3 = 12 + 9 = 21
\]
3. For the tenth term \( A(10) \):
\[
A(10) = 12 + (10 - 1)(3) = 12 + 9 \times 3 = 12 + 27 = 39
\]
Now, we have the first term: \( 12 \), the fourth term: \( 21 \), and the tenth term: \( 39 \).
Thus, the answer is:
**12, 21, 39**.
1. For the first term \( A(1) \):
\[
A(1) = 12 + (1 - 1)(3) = 12 + 0 = 12
\]
2. For the fourth term \( A(4) \):
\[
A(4) = 12 + (4 - 1)(3) = 12 + 3 \times 3 = 12 + 9 = 21
\]
3. For the tenth term \( A(10) \):
\[
A(10) = 12 + (10 - 1)(3) = 12 + 9 \times 3 = 12 + 27 = 39
\]
Now, we have the first term: \( 12 \), the fourth term: \( 21 \), and the tenth term: \( 39 \).
Thus, the answer is:
**12, 21, 39**.