{an} = {6.2,8.1,10.0,11.9...} 63.2 is what term ?

To find which term \( a_n = 63.2 \) corresponds to in the sequence \(\{6.2, 8.1, 10.0, 11.9, \ldots\}\), we first need to determine if the given sequence follows a certain pattern. By examining the sequence:

1. \( a_1 = 6.2 \)
2. \( a_2 = 8.1 \)
3. \( a_3 = 10.0 \)
4. \( a_4 = 11.9 \)

We notice that the difference between consecutive terms appears to be constant:

\[
\begin{align*}
a_2 - a_1 & = 8.1 - 6.2 = 1.9, \\
a_3 - a_2 & = 10.0 - 8.1 = 1.9, \\
a_4 - a_3 & = 11.9 - 10.0 = 1.9.
\end{align*}
\]

Since the common difference \( d \) is 1.9, this sequence is an **arithmetic sequence**.

The general formula for the \( n \)-th term of an arithmetic sequence is given by:

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

Substituting the values we know:

\[
63.2 = 6.2 + (n-1) \cdot 1.9
\]

Now, solve for \( n \):

\[
63.2 - 6.2 = (n-1) \cdot 1.9
\]

\[
57 = (n-1) \cdot 1.9
\]

\[
n-1 = \frac{57}{1.9}
\]

\[
n-1 = 30
\]

\[
n = 31
\]

Therefore, the term \( 63.2 \) is the **31st term** of the sequence.

Would you like more details or have any questions about this solution?

### Related Questions:

1. How would you find the 50th term of the sequence?
2. What is the sum of the first 31 terms of the sequence?
3. How can you verify that this sequence is arithmetic?
4. How do you find the common difference of an arithmetic sequence if the first term and another term are known?
5. What is the 100th term of this sequence?

### Tip:
In arithmetic sequences, knowing the first term and the common difference allows you to calculate any term in the sequence using the formula \( a_n = a_1 + (n-1) \cdot d \).

Learn how to find the 31st term of an arithmetic sequence with a common difference of 1.9. Detailed step-by-step solution using the arithmetic sequence nth term formula. Suitable for high school students studying arithmetic sequences.

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