Question

find the indicated term in each arithmetic sequence.
a_(21) for 10, 7, 4

Answer 1

To find the 21st term \( a_{21} \) in the arithmetic sequence given by the numbers \( 10, 7, 4 \), we first need to identify the first term and the common difference.

1. **Identify the first term \( a_1 \)**:
\[
a_1 = 10
\]

2. **Calculate the common difference \( d \)**:
The common difference can be found by subtracting the first term from the second term:
\[
d = a_2 - a_1 = 7 - 10 = -3
\]

3. **Use the formula for the \( n \)-th term of an arithmetic sequence**:
The formula for the \( n \)-th term \( a_n \) of an arithmetic sequence is given by:
\[
a_n = a_1 + (n - 1)d
\]
Substituting \( n = 21 \), \( a_1 = 10 \), and \( d = -3 \):
\[
a_{21} = 10 + (21 - 1)(-3)
\]
\[
= 10 + 20 \times (-3)
\]
\[
= 10 - 60
\]
\[
= -50
\]

Thus, the 21st term \( a_{21} \) of the sequence is \( -50 \).