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trapecia [35]
2 years ago
5

Please help me as soon as posable!! In hurry!!(24 points)

Mathematics
1 answer:
attashe74 [19]2 years ago
4 0

The sequence is geometric, so

a_n = r a_{n-1}

for some constant r. From this rule, it follows that

a_3 = r a_2 \implies 20 = 2r \implies r = 10

and we can determine the first term to be

a_2 = r a_1 \implies 2 = 10 a_1 \implies a_1 = \dfrac15

Now, by substitution we have

a_n = r a_{n-1} = r^2 a_{n-2} = r^3 a_{n-3} = \cdots

and so on down to (D)

a_n = r^{n-1} a_1 = 10^{n-1} \cdot \dfrac15

(notice how the exponent on r and the subscript on a add up to n)

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