Question

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 defined by the nth term \( a_n = 3 \cdot 2^{n-2} \), we will substitute \( n = 1 \), \( n = 2 \), and \( n = 3 \) into the equation.

1. For \( n = 1 \):
\[
a_1 = 3 \cdot 2^{1-2} = 3 \cdot 2^{-1} = 3 \cdot \frac{1}{2} = \frac{3}{2}
\]

2. For \( n = 2 \):
\[
a_2 = 3 \cdot 2^{2-2} = 3 \cdot 2^{0} = 3 \cdot 1 = 3
\]

3. For \( n = 3 \):
\[
a_3 = 3 \cdot 2^{3-2} = 3 \cdot 2^{1} = 3 \cdot 2 = 6
\]

Thus, the first three terms of the sequence are:
\[
\frac{3}{2}, \, 3, \, 6
\]