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V125BC [204]
3 years ago
8

Woo-Jin and Kiran were asked to find an explicit formula for the sequence 64\,,\,16\,,\,4\,,\,1,...64,16,4,1,...64, comma, 16, c

omma, 4, comma, 1, comma, point, point, point. Woo-Jin said the formula is f(n)
Mathematics
2 answers:
olya-2409 [2.1K]3 years ago
5 0

Answer:

f(n)=64(\frac{1}{4})^{n-1}

Step-by-step explanation:

The given sequence is

64, 16, 4, 1

r_1=\dfrac{a_2}{a_1}=\dfrac{16}{64}=\dfrac{1}{4}

r_2=\dfrac{a_3}{a_2}=\dfrac{4}{16}=\dfrac{1}{4}

r_3=\dfrac{a_4}{a_3}=\dfrac{1}{4}

It is a geometric series because it has a common ratio r_1=r_2=r_3=\dfrac{1}{4}.

First term is 64.

The explicit formula of a geometric series is

f(n)=ar^{n-1}

where, a is first term and r is common ratio.

Substitute a=64 and r=1/4 in the above function.

f(n)=64(\frac{1}{4})^{n-1}

Therefore, the required explicit formula is f(n)=64(\frac{1}{4})^{n-1}.

VLD [36.1K]3 years ago
4 0

Answer:

Neither Woo-Jin nor Kiran

Step-by-step explanation:

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