the explicit formula for aₙ the nth term of the sequence will be:
Step-by-step explanation:
The explicit formula of geometric sequence is of the form:

where a₁ is the first term and r is the common ratio.
We are given:
a₁ = 6
r = 2/3
Putting values in the formula:

So, the explicit formula for aₙ the nth term of the sequence will be: 
Keywords: Explicit formula for geometric sequence
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Answer:

Step-by-step explanation:
5x4+20x3-105x2
5x2( x^2 +4x -21)

Step-by-step explanation:
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The lowest rank of the class is unknown to us.
Let's say, it's x.
highest marks =2 × lowest rank + 7
=> 87 = 2x + 7 (this is the equation we gotta solve)
=> 87 - 7 = 2x
=> 2x = 80
=> x = 40
And x is the lowest rank of the class, so we got the required answer.

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it can be 17 since the denominators are in increasing order and 17 only fits in.
I'm looking for any other pattern that can be present here.
Answer:
13
Step-by-step explanation:
Take 18 minus 5 and the answer is 13.