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solmaris [256]
3 years ago
7

6th term 25,75,225,675,.... is it arithmetic or geometric. what's the explicit equation and the given term​

Mathematics
1 answer:
Alenkinab [10]3 years ago
7 0

Answer:

see explanation

Step-by-step explanation:

There is a common ratio r between consecutive terms, that is

\frac{a_{2} }{a_{1} } = \frac{75}{25} = 3

\frac{a_{3} }{a_{2} } = \frac{225}{75} = 3

\frac{a_{4} }{a_{3} } = \frac{675}{225} = 3

This indicates the sequence is geometric with explicit formula

a_{n}  = a₁ (r)^{n-1}

where a₁ is the first term and r the common ratio

Here a₁ = 25 and r = 3 , then

a₆ = 25 × 3^{5} = 25 × 243 = 6075

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