Question

What is the 300th term

57,66,75,84,93

Answer 1

To find the 300th term of the sequence \(57, 66, 75, 84, 93\), we first need to identify a pattern in the given sequence.

Looking at the terms:
- The first term is \(57\).
- The second term is \(66\).
- The third term is \(75\).
- The fourth term is \(84\).
- The fifth term is \(93\).

Now, let's calculate the differences between consecutive terms:
- \(66 - 57 = 9\)
- \(75 - 66 = 9\)
- \(84 - 75 = 9\)
- \(93 - 84 = 9\)

The common difference is \(9\). This indicates that the sequence is an arithmetic series.

The general formula for the \(n\)-th term of an arithmetic series can be expressed as:
\[
a_n = a + (n-1)d
\]
where:
- \(a\) is the first term,
- \(d\) is the common difference,
- \(n\) is the term number.

In this case, we have:
- \(a = 57\),
- \(d = 9\).

Now, substituting \(n = 300\) into the formula:
\[
a_{300} = 57 + (300 - 1) \times 9
\]
\[
a_{300} = 57 + 299 \times 9
\]
First, calculate \(299 \times 9\):
\[
299 \times 9 = 2691
\]
Now substitute this back into the equation:
\[
a_{300} = 57 + 2691 = 2748
\]

Thus, the 300th term is \(\boxed{2748}\).