Question

Use the explicit formula an = a1 + (n - 1) • d to find the 500th term of the sequence below.
..24. 31,38, 45,52
A. 3493
B. 3545
C. 3517
D. 3524

Answer 1

To find the 500th term of the arithmetic sequence given, we can identify the first term \( a_1 \) and the common difference \( d \).

1. **Identify the first term**:
The first term \( a_1 \) is 24.

2. **Identify the common difference**:
To find \( d \), we can subtract consecutive terms:
\[
d = 31 - 24 = 7
\]
(We can confirm this with the other consecutive terms: \( 38 - 31 = 7 \), \( 45 - 38 = 7 \), and \( 52 - 45 = 7 \)).

3. **Use the explicit formula**:
The explicit formula for the \( n \)-th term of an arithmetic sequence is given by:
\[
a_n = a_1 + (n - 1) \cdot d
\]
Substituting the known values:
\[
a_{500} = 24 + (500 - 1) \cdot 7
\]

4. **Calculate**:
\[
a_{500} = 24 + 499 \cdot 7
\]
Calculate \( 499 \cdot 7 \):
\[
499 \cdot 7 = 3493
\]
Now substitute back into the equation:
\[
a_{500} = 24 + 3493 = 3517
\]

Thus, the 500th term of the sequence is \(\boxed{3517}\).