Find the first three terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.

Question

an = 10(10)n

Answer 1

To find the first three terms of the sequence defined by \( a_n = 10(10^n) \), we will evaluate it for \( n = 1 \), \( n = 2 \), and \( n = 3 \).

1. For \( n = 1 \): \[ a_1 = 10(10^1) = 10(10) = 100 \]

2. For \( n = 2 \): \[ a_2 = 10(10^2) = 10(100) = 1000 \]

3. For \( n = 3 \): \[ a_3 = 10(10^3) = 10(1000) = 10000 \]

Thus, the first three terms of the sequence are: \[ 100, 1000, 10000 \]