Write the first five terms of the geometric sequence with the first term, [tex]$a_1=4$[/tex], and common ratio, [tex]$r=3$[/tex].

The first term is [tex]\boxed{4}[/tex] (Type an integer or a simplified fraction.)



Answer :

To find the first five terms of the geometric sequence with the first term [tex]\( a_1 = 4 \)[/tex] and the common ratio [tex]\( r = 3 \)[/tex], we use the formula for the [tex]\( n \)[/tex]-th term of a geometric sequence:

[tex]\[ a_n = a_1 \cdot r^{n-1} \][/tex]

Let's calculate each term step-by-step:

1. First term ([tex]\(a_1\)[/tex]):
[tex]\[ a_1 = 4 \][/tex]

2. Second term ([tex]\(a_2\)[/tex]):
[tex]\[ a_2 = a_1 \cdot r = 4 \cdot 3 = 12 \][/tex]

3. Third term ([tex]\(a_3\)[/tex]):
[tex]\[ a_3 = a_1 \cdot r^2 = 4 \cdot (3^2) = 4 \cdot 9 = 36 \][/tex]

4. Fourth term ([tex]\(a_4\)[/tex]):
[tex]\[ a_4 = a_1 \cdot r^3 = 4 \cdot (3^3) = 4 \cdot 27 = 108 \][/tex]

5. Fifth term ([tex]\(a_5\)[/tex]):
[tex]\[ a_5 = a_1 \cdot r^4 = 4 \cdot (3^4) = 4 \cdot 81 = 324 \][/tex]

Therefore, the first five terms of the geometric sequence are:

[tex]\[ 4, 12, 36, 108, 324 \][/tex]

So, the first term is [tex]\(\boxed{4}\)[/tex].