Respuesta :
a1=3, a2=3*6, a3=3*6*6
[tex]a_{n}=a_{1}*6^{n-1} a_{n}=3*6^{n-1} a_{n}= \frac{3*6^{n}}{6} = \frac{6^{n}}{2} a_{n}= \frac{6^{n}}{2} [/tex]
[tex]a_{n}=a_{1}*6^{n-1} a_{n}=3*6^{n-1} a_{n}= \frac{3*6^{n}}{6} = \frac{6^{n}}{2} a_{n}= \frac{6^{n}}{2} [/tex]
Answer:
[tex]a_n=3\times 6^{n-1}\\\\a_n=\frac{6^n}{2}[/tex]
Step-by-step explanation:
This is a geometric sequence, since each term is found by multiplying the previous term by a constant (called the common ratio).
The explicit formula for a geometric sequence is
[tex]a_n=a_1\times r^{n-1}[/tex], where a₁ is the first term and r is the common ratio.
In this sequence, the first term is 3 and the common ratio is 6; this gives us
[tex]a_n=3\times 6^{n-1}[/tex]
Using the product property of exponents, we can write the power of 6 as
[tex]a_n=3\times 6^n\times 6^{-1}[/tex]
Something raised to the -1 power is "flipped"; since 6 = 6/1, this means we have 1/6:
[tex]a_n=3\times 6^n\times \frac{1}{6}[/tex]
Using the commutative property, we multiply the 3 and the 1/6:
[tex]a_n=\frac{3}{6}\times 6^n[/tex]
Simplifying, we have
[tex]a_n=\frac{6^n}{2}[/tex]
