Let's analyze the given sequence with the initial term and recursive formula to find the first five terms.
The initial term is given by:
[tex]\[ a_1 = 1 \][/tex]
Now, we use the recursive formula to find the subsequent terms:
[tex]\[ a_{n+1} = \frac{a_n}{n+5} \][/tex]
We start from [tex]\( n = 1 \)[/tex] and proceed step by step:
1. For [tex]\( n = 1 \)[/tex]:
[tex]\[ a_2 = \frac{a_1}{1+5} = \frac{1}{6} \][/tex]
So, the second term is [tex]\( \frac{1}{6} \)[/tex].
2. For [tex]\( n = 2 \)[/tex]:
[tex]\[ a_3 = \frac{a_2}{2+5} = \frac{\frac{1}{6}}{7} = \frac{1}{6 \times 7} = \frac{1}{42} \][/tex]
So, the third term is [tex]\( \frac{1}{42} \)[/tex].
3. For [tex]\( n = 3 \)[/tex]:
[tex]\[ a_4 = \frac{a_3}{3+5} = \frac{\frac{1}{42}}{8} = \frac{1}{42 \times 8} = \frac{1}{336} \][/tex]
So, the fourth term is [tex]\( \frac{1}{336} \)[/tex].
4. For [tex]\( n = 4 \)[/tex]:
[tex]\[ a_5 = \frac{a_4}{4+5} = \frac{\frac{1}{336}}{9} = \frac{1}{336 \times 9} = \frac{1}{3024} \][/tex]
So, the fifth term is [tex]\( \frac{1}{3024} \)[/tex].
Therefore, the first five terms of the sequence are:
[tex]\[ 1, \frac{1}{6}, \frac{1}{42}, \frac{1}{336}, \frac{1}{3024} \][/tex]
Thus, the correct answer is:
B. [tex]\( \boxed{1, \frac{1}{6}, \frac{1}{42}, \frac{1}{336}, \frac{1}{3024}} \)[/tex]
