Question

Find the first four terms of the swquence gived by the following
a_(n)=9(2)^(n-1), n=1, 2, 3...

Answer 1

To find the first four terms of the sequence given by \( a_n = 9 \cdot 2^{n-1} \), we will substitute \( n = 1, 2, 3, \) and \( 4 \) into the formula.

1. For \( n = 1 \):
\[
a_1 = 9 \cdot 2^{1-1} = 9 \cdot 2^0 = 9 \cdot 1 = 9
\]

2. For \( n = 2 \):
\[
a_2 = 9 \cdot 2^{2-1} = 9 \cdot 2^1 = 9 \cdot 2 = 18
\]

3. For \( n = 3 \):
\[
a_3 = 9 \cdot 2^{3-1} = 9 \cdot 2^2 = 9 \cdot 4 = 36
\]

4. For \( n = 4 \):
\[
a_4 = 9 \cdot 2^{4-1} = 9 \cdot 2^3 = 9 \cdot 8 = 72
\]

The first four terms of the sequence are:
\[
9, 18, 36, 72
\]