Question

Find the 99th term of the arithmetic sequence 2,−3,−8,...(1 point)
a99=

Answer 1

To find the 99th term of the arithmetic sequence \(2, -3, -8, \ldots\), we first need to determine the first term and the common difference.

1. The first term \(a_1\) is:
\[
a_1 = 2
\]

2. The second term \(a_2\) is:
\[
a_2 = -3
\]
The common difference \(d\) can be calculated as:
\[
d = a_2 - a_1 = -3 - 2 = -5
\]

Now that we have the first term \(a_1 = 2\) and the common difference \(d = -5\), we can use the formula for the \(n\)-th term of an arithmetic sequence:
\[
a_n = a_1 + (n - 1)d
\]
To find the 99th term (\(a_{99}\)):
\[
a_{99} = a_1 + (99 - 1)d
\]
Substituting the values:
\[
a_{99} = 2 + (98)(-5)
\]
Calculating the value:
\[
a_{99} = 2 + (98 \times -5)
\]
\[
a_{99} = 2 - 490
\]
\[
a_{99} = -488
\]

Thus, the 99th term of the arithmetic sequence is:
\[
\boxed{-488}
\]