Respuesta :
The correct answer is
[tex]a_n=-4(a_{n-1}), a_1=7[/tex]
The explicit formula is of the form
[tex]a_n=a_1(r)^{n-1}[/tex],
where a₁ is the first term and r is the common ratio. Comparing this to our explicit form, we see that r = -4 and a₁ = 7.
The recursive formula is of the form
[tex]a_n=a_{n-1}*r[/tex]; using r=-4 gives us
[tex]a_n=-4(a_{n-1}), a_1=7[/tex]
[tex]a_n=-4(a_{n-1}), a_1=7[/tex]
The explicit formula is of the form
[tex]a_n=a_1(r)^{n-1}[/tex],
where a₁ is the first term and r is the common ratio. Comparing this to our explicit form, we see that r = -4 and a₁ = 7.
The recursive formula is of the form
[tex]a_n=a_{n-1}*r[/tex]; using r=-4 gives us
[tex]a_n=-4(a_{n-1}), a_1=7[/tex]
Answer:
Option (a) is correct.
The recursive rule for the given sequence [tex]a_n=7(-4)^{n-1}[/tex] is [tex]a_n = (-4)\cdot a_{n-1}[/tex] with [tex]a_1=7[/tex]
Step-by-step explanation:
The explicit sequence of the geometric sequence is given by:
[tex]a_n = a_1r^{n-1}[/tex]
where,
[tex]a_1[/tex] is the first term
r is the common ratio
n is the number of terms
For the given explicit rule, [tex]a_n=7(-4)^{n-1}[/tex]
Comparing with above sequence , we have,
[tex]a_1=7[/tex] and r = -4
Recursive formula for the geometric sequence having [tex]a_1=7[/tex] and r = -4 is given by:
[tex]a_n=r\cdot a_{n-1} \ for\ n\geq 2[/tex]
Putting values, we get,
[tex]a_n = (-4)\cdot a_{n-1}[/tex]
Hence, the recursive rule for the given sequence [tex]a_n=7(-4)^{n-1}[/tex] is [tex]a_n = (-4)\cdot a_{n-1}[/tex] with [tex]a_1=7[/tex]
hence, option (a) is correct.
