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

Question

an = 6(10)n

Answer 1

To find the first four terms of the sequence defined by \( a_n = 6(10)^n \), we will substitute \( n = 1, 2, 3, \) and \( 4 \) into the formula.

1. For \( n = 1 \): \[ a_1 = 6(10)^1 = 6(10) = 60 \]

2. For \( n = 2 \): \[ a_2 = 6(10)^2 = 6(100) = 600 \]

3. For \( n = 3 \): \[ a_3 = 6(10)^3 = 6(1000) = 6000 \]

4. For \( n = 4 \): \[ a_4 = 6(10)^4 = 6(10000) = 60000 \]

Thus, the first four terms of the sequence are:

1. \( a_1 = 60 \)
2. \( a_2 = 600 \)
3. \( a_3 = 6000 \)
4. \( a_4 = 60000 \)

So, the first four terms are \( 60, 600, 6000, 60000 \).