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).
260, comma, 255, comma, 250, comma, dot dot dot
260,255,250,...
Find the 43rd term.
260, comma, 255, comma, 250, comma, dot dot dot
260,255,250,...
Find the 43rd term.
Answers
GPT-4o mini
To find the 43rd term of the sequence given by 260, 255, 250, ..., we first observe the pattern in the sequence.
The first three terms are:
- 1st term: 260
- 2nd term: 255
- 3rd term: 250
We can see that each term decreases by 5 from the previous term. This indicates that the sequence is an arithmetic sequence with the first term \( a = 260 \) and a common difference \( d = -5 \).
The formula for the \( n \)-th term of an arithmetic sequence is given by:
\[
a_n = a + (n-1)d
\]
We want to find the 43rd term (\( n = 43 \)):
\[
a_{43} = 260 + (43 - 1)(-5)
\]
\[
a_{43} = 260 + 42 \times (-5)
\]
\[
a_{43} = 260 - 210
\]
\[
a_{43} = 50
\]
Thus, the 43rd term of the sequence is \( \boxed{50} \).
The first three terms are:
- 1st term: 260
- 2nd term: 255
- 3rd term: 250
We can see that each term decreases by 5 from the previous term. This indicates that the sequence is an arithmetic sequence with the first term \( a = 260 \) and a common difference \( d = -5 \).
The formula for the \( n \)-th term of an arithmetic sequence is given by:
\[
a_n = a + (n-1)d
\]
We want to find the 43rd term (\( n = 43 \)):
\[
a_{43} = 260 + (43 - 1)(-5)
\]
\[
a_{43} = 260 + 42 \times (-5)
\]
\[
a_{43} = 260 - 210
\]
\[
a_{43} = 50
\]
Thus, the 43rd term of the sequence is \( \boxed{50} \).