Question

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

Answer 1

To find the 99th term of the arithmetic sequence 2, -3, -8,..., we first need to identify the first term and the common difference.

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

2. To find the common difference \( d \), we can subtract the first term from the second term:
\[
d = a_2 - a_1 = -3 - 2 = -5
\]

Now we have:
- First term \( a_1 = 2 \)
- Common difference \( d = -5 \)

The formula for the \( n \)-th term of an arithmetic sequence is given by:
\[
a_n = a_1 + (n-1)d
\]

To find the 99th term (\( n = 99 \)):
\[
a_{99} = a_1 + (99 - 1)d
\]
\[
a_{99} = 2 + (98)(-5)
\]
\[
a_{99} = 2 - 490
\]
\[
a_{99} = 2 - 490 = -488
\]

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