write the explit term of a(subscript)100th=3(subscript)1(9)^(n-1)

Answer 1

To find the explicit term of the sequence given by \( a_{100} = 3 \cdot 1 \cdot 9^{(n-1)} \), we can rewrite the formula. The term \( a_n \) for general \( n \) based on the provided formula would actually be:

\[ a_n = 3 \cdot 1 \cdot 9^{(n-1)} = 3 \cdot 9^{(n-1)} \]

Now, we need to find \( a_{100} \):

\[ a_{100} = 3 \cdot 9^{(100-1)} = 3 \cdot 9^{99} \]

Thus, the explicit term \( a_{100} \) is:

\[ a_{100} = 3 \cdot 9^{99} \]

If further simplifications are needed, since \( 9 \) can be expressed as \( 3^2 \), we could express \( a_{100} \) as:

\[ a_{100} = 3 \cdot (3^2)^{99} = 3 \cdot 3^{198} = 3^{199} \]

So the explicit term \( a_{100} \) can also be represented as:

\[ a_{100} = 3^{199} \]