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Virty [35]
3 years ago
5

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Mathematics
1 answer:
olasank [31]3 years ago
4 0

Answer:  a_n=2(5)^{n-2}

<u>Step-by-step explanation:</u>

The explicit rule for a geometric sequence is: a_n=a_1(r)^{n-1}\quad \text{where}\ a_1\ \text{is the first term and r is the ratio}

The information provided is: a₁ = \dfrac{2}{5}  and  r = 5

a_n=\dfrac{2}{5}(5)^{n - 1}\\\\.\quad = 2(5)^{n-2}

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Klio2033 [76]

Answer:

a) a_n=2(a_{n-1}), where a_1=5.

b)  a_n=5(2)^{n-1}

Step-by-step explanation:

The given sequence is


5,10,20,40....


The first term of the sequence is

a_1=5


The second term is a_2=10


The common ratio for this sequence can be determined using any two consecutive terms in the sequence.

Using the first two terms, the common ratio is

r=\frac{a_2}{a_1}


\Rightarrow r=\frac{10}{5}=2


a) The recursive rule is given by,


a_n=r(a_{n-1})


a_n=2(a_{n-1}), where a_1=5.


b) The explicit rule is given by a_n=a_1r^{n-1}


\Rightarrow a_n=5(2)^{n-1}





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