Sure, let's clarify the calculation of the terms in the sequence step by step. The given sequence is described by the term [tex]\((n^3) + 2\)[/tex], where [tex]\(n\)[/tex] is the position in the sequence.
1. Second Term:
- Position [tex]\(n = 2\)[/tex]
- Applying the formula: [tex]\((2^3) + 2 = 8 + 2 = 10\)[/tex]
- So, the second term is [tex]\(10\)[/tex].
2. Fourth Term:
- Position [tex]\(n = 4\)[/tex]
- Applying the formula: [tex]\((4^3) + 2 = 64 + 2 = 66\)[/tex]
- So, the fourth term is [tex]\(66\)[/tex].
3. Sixth Term:
- Position [tex]\(n = 6\)[/tex]
- Applying the formula: [tex]\((6^3) + 2 = 216 + 2 = 218\)[/tex]
- So, the sixth term is [tex]\(218\)[/tex].
4. Eighth Term:
- Position [tex]\(n = 8\)[/tex]
- Applying the formula: [tex]\((8^3) + 2 = 512 + 2 = 514\)[/tex]
- So, the eighth term is [tex]\(514\)[/tex].
5. Tenth Term:
- Position [tex]\(n = 10\)[/tex]
- Applying the formula: [tex]\((10^3) + 2 = 1000 + 2 = 1002\)[/tex]
- So, the tenth term is [tex]\(1002\)[/tex].
[tex]\[
\begin{tabular}{|l|c|c|c|c|c|c|}
\hline
n \text{ (Position in sequence)} & 2 & 4 & 6 & 8 & 10 & n \\
\hline
\text{Value of term} & 10 & 66 & 218 & 514 & 1002 & \text{(nth term)} \\
\hline
\end{tabular}
\][/tex]
To summarize:
- Second term: [tex]\(10\)[/tex]
- Fourth term: [tex]\(66\)[/tex]
- Sixth term: [tex]\(218\)[/tex]
- Eighth term: [tex]\(514\)[/tex]
- Tenth term: [tex]\(1002\)[/tex]
These values align with our calculations, and you can use the same process to calculate any nth term using the formula [tex]\((n^3) + 2\)[/tex].
