Answer:
14- The given sequence has common ratio = [tex]\frac{1}{2}[/tex], so it is a geometric sequence.
15- explicit : [tex]a_{n}=10(1.5)^{n-1}[/tex], recursive : [tex]a_{n}=1.5\times a_{n-1}[/tex]
Step-by-step explanation:
Ques 14: We have the sequence, [tex]18,9,\frac{9}{2},\frac{9}{4},\frac{9}{8},...[/tex].
So, we will find the common ratio of the given sequence,
i.e. Common ratio = [tex]\frac{9}{18}=\frac{\frac{9}{2}}{9}=..=\frac{1}{2}[/tex]
Thus, we have,
The given sequence has common ratio = [tex]\frac{1}{2}[/tex], so it is a geometric sequence.
Ques 15: We have the sequence, [tex]10,15,22.5,33.75,...[/tex]
As, the common ratio of the given sequence = [tex]\frac{15}{10}=\frac{22.5}{15}=...=1.5[/tex]
Thus, the explicit form is given by, [tex]a_{n}=a_{1}(r)^{n-1}[/tex] i.e. [tex]a_{n}=10(1.5)^{n-1}[/tex].
Also, the recursive form is given by, [tex]a_{n}=r\times a_{n-1}[/tex] i.e. [tex]a_{n}=1.5\times a_{n-1}[/tex].
