Question

Find the first four terms and the 100 th term of the sequence. aₙ = nⁿ

Answer 1

The first four terms of the sequence \(a_n = n^n\) are:

1. \(a_1 = 1^1 = 1\)
2. \(a_2 = 2^2 = 4\)
3. \(a_3 = 3^3 = 27\)
4. \(a_4 = 4^4 = 256\)

To find the 100th term (\(a_{100}\)), it would be \(100^{100}\), which is a very large number. If you need the specific value, I can calculate it for you.

Answer 2

First four terms of the sequence an = nn are 1, 4, 27, and 256 respectively. The 100th term is 100100, which is an exceedingly large number and requires electronic computation.

Step-by-step explanation:

To find the first four terms and the 100th term of the sequence where the nth term is given by an = nn, we substitute n with the position of the term we want to find. For the first four terms, we have:

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To find the 100th term, a100, we calculate 100100. This is an extremely large number and is normally computed using a calculator or computer.