The nth term of a sequence is given by 3.2^n-2. write down the first three term of the sequence

Answer 1

To find the first three terms of the sequence given by the nth term \( a_n = 3 \cdot 2^n - 2 \), we will calculate the values for \( n = 1, 2, \) and \( 3 \):

1. For \( n = 1 \): \[ a_1 = 3 \cdot 2^1 - 2 = 3 \cdot 2 - 2 = 6 - 2 = 4 \]

2. For \( n = 2 \): \[ a_2 = 3 \cdot 2^2 - 2 = 3 \cdot 4 - 2 = 12 - 2 = 10 \]

3. For \( n = 3 \): \[ a_3 = 3 \cdot 2^3 - 2 = 3 \cdot 8 - 2 = 24 - 2 = 22 \]

Thus, the first three terms of the sequence are:

1. \( 4 \)
2. \( 10 \)
3. \( 22 \)

So, the first three terms are \( 4, 10, \) and \( 22 \).