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).
253, comma, 248, comma, 243, comma, dot dot dot
253,248,243,...
Find the 49th term.

Answer 1

The sequence given is as follows: 253, 248, 243, ...

To find the pattern, we can observe the differences between consecutive terms:

- From 253 to 248: 253 - 248 = 5
- From 248 to 243: 248 - 243 = 5

The sequence shows a constant decrease of 5 for each term. Therefore, we can say that this is an arithmetic sequence with a first term \( a_1 = 253 \) and a common difference \( d = -5 \).

The formula for the \( n \)-th term of an arithmetic sequence is given by:

\[
a_n = a_1 + (n - 1) \cdot d
\]

For our sequence:

- \( a_1 = 253 \)
- \( d = -5 \)

Now we want to find the 49th term (\( n = 49 \)):

\[
a_{49} = 253 + (49 - 1) \cdot (-5)
\]

Calculating it step-by-step:

1. Calculate \( 49 - 1 = 48 \).
2. Calculate \( 48 \cdot (-5) = -240 \).
3. Add this to the first term:

\[
a_{49} = 253 - 240 = 13
\]

Thus, the 49th term is

\[
\boxed{13}
\]