Answer:
The [tex]10^{th}[/tex] term of the given sequence
[tex]t_{10} = \frac{5^{9} }{2^{8} }[/tex]
Step-by-step explanation:
Step(i):-
Given sequence 2 , 5, [tex]\frac{25}{2}[/tex]
First term a = 2
The difference of given geometric sequence
[tex]d = \frac{r_{2} }{r_{1} } = \frac{5}{2}[/tex]
Step(ii):-
The [tex]n^{th}[/tex] term of the given sequence
[tex]t_{n} = ar^{n-1}[/tex]
The [tex]10^{th}[/tex] term of the given sequence
[tex]t_{10} = (2)(\frac{5}{2} )^{10-1}[/tex]
[tex]t_{10} = (2)(\frac{5}{2} )^{9}= \frac{5^{9} }{2^{8} }[/tex]
