How do you determine if a pair of lines are parallel? For example, the lines -3x+8y=24 and 3x-8y=7?
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The number of permutations of picking 4 pens from the box is 30.
There are six different unique colored pens in a box.
We have to select four pens from the different unique colored pens.
We have to find in how many different orders the four pens can be selected.
<h3>What is a permutation?</h3>A permutation is the number of different arrangements of a set of items in a particular definite order.
The formula used for permutation of n items for r selection is:
Where n! = n(n-1)(n-2)(n-3)..........1 and r! = r(r-1)(r-2)(r-3)........1
We have,
Number of colored pens = 6
n = 6.
Number of pens to be selected = 4
r = 4
Applying the permutation formula.
We get,
=
= 6! / 4!
=(6x5x4x3x2x1 ) / ( 4x3x2x1)
= 6x5
=30
Thus the number of permutations of picking 4 pens from a total of 6 unique colored pens in the box is 30.
Learn more about permutation here:
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Given:
The given sequence is:
To find:
The recursive formula for , the nth term of the sequence.
Solution:
We have,
Here, the first term is 5.
The common difference is -7.
The recursive formula for the nth term of the sequence is
Where, is the common difference.
Putting in the above formula, we get
Therefore, the recursive formula for the nth term of the sequence is .