Question

Use the explicit formula an = a1 + (n- 1) • d to find the 300th term of the sequence below.
57, 66, 75,84, 93, ...
a1= ______
n= _____
d = _____
300th term is _____

:: 300
:: 57
:2748
:: 9

Answer 1

To find the 300th term of the arithmetic sequence given by the terms 57, 66, 75, 84, 93, ..., we can use the explicit formula for the n-th term of an arithmetic sequence:

\[ a_n = a_1 + (n - 1) \cdot d \]

Where:
- \( a_1 \) is the first term of the sequence.
- \( n \) is the term number we want to find.
- \( d \) is the common difference between consecutive terms.

From the sequence:
- The first term \( a_1 = 57 \).
- To find the common difference \( d \), we can subtract the first term from the second term (or any two consecutive terms):
\( d = 66 - 57 = 9 \).

Now, we have:
- \( a_1 = 57 \)
- \( d = 9 \)
- \( n = 300 \)

Using the explicit formula to find the 300th term:

\[
a_{300} = 57 + (300 - 1) \cdot 9
\]
\[
a_{300} = 57 + 299 \cdot 9
\]
\[
a_{300} = 57 + 2691
\]
\[
a_{300} = 2748
\]

Thus, the filled values are:
- \( a_1 = 57 \)
- \( n = 300 \)
- \( d = 9 \)
- The 300th term is \( 2748 \).