Answer:
B
Step-by-step explanation:
This is a geometric sequence with common ratio r and n th term
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term
r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex]
r = [tex]\frac{\sqrt{10} }{\sqrt{5} }[/tex] = [tex]\sqrt{\frac{10}{2} }[/tex] = [tex]\sqrt{2}[/tex]
The first term a = [tex]\sqrt{5}[/tex]
[tex]a_{9}[/tex] = [tex]\sqrt{5}[/tex] × [tex](\sqrt{2}) ^{8}[/tex]
[ Note [tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 2 ], hence
[tex](\sqrt{2}) ^{8}[/tex] = 2 × 2 × 2 × 2 = 16
⇒ [tex]a_{9}[/tex] = 16[tex]\sqrt{5}[/tex] → B
The 9th term of the sequence √5, √10, 2√5,... is 16√5.
A geometric progression is a type of progression in which the common quotient between any two consecutive numbers is the same. It can be written as:
a_n = ar^(n-1)
The sequence is √5, √10, 2√5,...
From this, we can see that:
a = √5
r = √10/√5 = √2
n = 9
We have to substitute the values in the general form of a geometric progression to find the 9th term.
a_n = ar^(n-1)
⇒ a_9 = (√5)(√2)^(9-1)
= (√5)(√2)^8
= 16√5
Therefore, we have found the 9th term of the sequence √5, √10, 2√5,... to be 16√5.
Learn more about geometric progression here: https://brainly.com/question/12006112
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