Question
The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).
13, comma, 17, comma, 21, comma, dot dot dot
13,17,21,...
Find the 43rd term.
Find the 43rd term.
13, comma, 17, comma, 21, comma, dot dot dot
13,17,21,...
Find the 43rd term.
Find the 43rd term.
Answers
GPT-4o mini
To find the 43rd term in the sequence given by the terms 13, 17, 21, ..., we first identify the pattern or formula for the sequence.
We can observe that the sequence is an arithmetic sequence where the first term \( a_1 = 13 \) and the common difference \( d \) can be calculated as follows:
\[
d = 17 - 13 = 4
\]
Now that we know the first term and the common difference, we can use the formula for the \( n \)-th term of an arithmetic sequence:
\[
a_n = a_1 + (n - 1) \cdot d
\]
We want to find the 43rd term (\( n = 43 \)):
\[
a_{43} = 13 + (43 - 1) \cdot 4
\]
Calculating:
\[
a_{43} = 13 + 42 \cdot 4
\]
\[
a_{43} = 13 + 168
\]
\[
a_{43} = 181
\]
Therefore, the 43rd term of the sequence is \(\boxed{181}\).
We can observe that the sequence is an arithmetic sequence where the first term \( a_1 = 13 \) and the common difference \( d \) can be calculated as follows:
\[
d = 17 - 13 = 4
\]
Now that we know the first term and the common difference, we can use the formula for the \( n \)-th term of an arithmetic sequence:
\[
a_n = a_1 + (n - 1) \cdot d
\]
We want to find the 43rd term (\( n = 43 \)):
\[
a_{43} = 13 + (43 - 1) \cdot 4
\]
Calculating:
\[
a_{43} = 13 + 42 \cdot 4
\]
\[
a_{43} = 13 + 168
\]
\[
a_{43} = 181
\]
Therefore, the 43rd term of the sequence is \(\boxed{181}\).