Answer:
[tex]\frac{1215}{32}[/tex]
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex], hence
[tex]a_{6}[/tex] = 5 × [tex](\frac{3}{2 )} ^{5}[/tex] = 5 × [tex]\frac{243}{32}[/tex] = [tex]\frac{1215}{32}[/tex]
The sixth term of the geometric sequence is 1215/32 given that the first term a₁=5 and common ratio r=3/2. This can be obtained by using formula for nth term of the geometric sequence.
Sequence is s collection of objects in a particular order and repetitions are allowed.
Geometric Sequence:
a, ar, ar¹, ..., arⁿ⁻¹ is a geometric sequence, where a is the first term, r is the common ratio and arⁿ⁻¹ is the nth term.
From the definition, nth term of a geometric sequence is arⁿ⁻¹.
Given that, a₁=5 and r=3/2
To find sixth term, put n=6 ⇒ arⁿ⁻¹=(5)(3/2)⁶⁻¹
=(5)(3/2)⁵
=5(3⁵/2⁵)
=5×(243/32)
=1215/32
Hence the sixth term of the geometric sequence is 1215/32 given that the first term a₁=5 and common ratio r=3/2.
Learn more about geometric sequence here:
brainly.com/question/2959141
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