Question

The explicit rule for a sequence is an=7(−4)n−1

Answer 1

The correct answer is

$a_n=-4(a_{n-1}), a_1=7$

The explicit formula is of the form
$a_n=a_1(r)^{n-1}$, 
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
$a_n=a_{n-1}*r$; using r=-4 gives us
$a_n=-4(a_{n-1}), a_1=7$

Answer 2

Answer:

Option (a) is correct.

The recursive rule for the given sequence $a_n=7(-4)^{n-1}$ is $a_n = (-4)\cdot a_{n-1}$ with $a_1=7$

Step-by-step explanation:

The explicit sequence of the geometric sequence is given by:

$a_n = a_1r^{n-1}$  

where,  

$a_1$ is the first term

r is the common ratio  

n is the number of terms

For the given explicit rule, $a_n=7(-4)^{n-1}$

Comparing with above sequence , we have,

$a_1=7$ and r = -4

Recursive formula for the geometric sequence having $a_1=7$ and r = -4  is given by:

$a_n=r\cdot a_{n-1} \ for\ n\geq 2$

Putting values, we get,

$a_n = (-4)\cdot a_{n-1}$

Hence, the recursive rule for the given sequence $a_n=7(-4)^{n-1}$ is $a_n = (-4)\cdot a_{n-1}$ with $a_1=7$

hence, option (a) is correct.