Write an explicit formula for an,the Nth term of the sequence 4,12,36
1 answer:
Answer:
Step-by-step explanation:
Since the sequence is geometric (it multiplies the previous number each time). The nth term sequence would be
Because the sequence multiplies by 3 each time, The base number in that equation would be .
So of the equation would be:
.
Compare the 2 equations:
4, 12, 36
3, 9 ,27
The difference between the 2 equations is: 1, 3, 9 which itself is a geometric sequence so the nth term of this new equation is: .
Combine these 2 equations together and you get:
.
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The perimeter, by definition, is the outside measure of that figure. MN and LM are the same length and LK and NK are the same length....we just need to find the lengths! Use the distance formula to find the distance between the 2 points:
For the segment MN, use the coordinates of M as your x1, y1, and use the coordinates of N for x2, y2:
which simplifies to
which is 
So that is the length of both MN and LM. So far our perimeter is
Now let's use the same formula to find out the length of one of the longer segments:
which simplifies down to
which is of course
Since we have 2 of those lengths,
So our perimeter is, in the end,
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For the segment MN, use the coordinates of M as your x1, y1, and use the coordinates of N for x2, y2:
which simplifies to
So that is the length of both MN and LM. So far our perimeter is
Now let's use the same formula to find out the length of one of the longer segments:
which simplifies down to
which is of course
Since we have 2 of those lengths,
So our perimeter is, in the end,
That's the third choice down