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).
360, comma, 353, comma, 346, comma, dot dot dot
360,353,346,...
Find the 40th term.
Find the 40th term.

Answer 1

To find the 40th term of the sequence given by the first three terms \(360\), \(353\), and \(346\), we need to determine the pattern in the sequence.

The difference between each term can be calculated as follows:

- The difference between the 1st term (360) and the 2nd term (353) is:
\[
360 - 353 = 7
\]

- The difference between the 2nd term (353) and the 3rd term (346) is:
\[
353 - 346 = 7
\]

From this, we can see that the sequence decreases by 7 each time. Thus, we can express the \(n\)-th term of the sequence with the formula:
\[
a_n = 360 - 7(n - 1)
\]

Here, \(a_n\) is the nth term of the sequence. We need to find the 40th term, \(a_{40}\):
\[
a_{40} = 360 - 7(40 - 1)
\]

Calculating \(40 - 1\):
\[
40 - 1 = 39
\]

Next, calculate \(7 \times 39\):
\[
7 \times 39 = 273
\]

Now plug this back into the formula:
\[
a_{40} = 360 - 273
\]

Calculating that gives:
\[
360 - 273 = 87
\]

Thus, the 40th term of the sequence is:
\[
\boxed{87}
\]