What should I do to get both numeric terms are on the right side of the equation. 3/2t - 4/3t - 16 = - 6
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We can find the number of extra clubs in the deck from the given probability, since the probability of drawing a diamond and a club is
but this would imply that
, which suggests we're taking 4 clubs out of the original deck and contradicts the problem statement that there are "too many clubs".
Perhaps the question is providing the probability of drawing a diamond, THEN a club, or vice versa. In that case, we have
and solving gives
, which makes more sense. Then the number of extra spades in the deck must be 2.
but this would imply that
Perhaps the question is providing the probability of drawing a diamond, THEN a club, or vice versa. In that case, we have
and solving gives
We can find a formula for nth term of the given sequence as follows:
1, 5, 12, 22, 35
The 1st differences between terms:
4, 7, 10, 13
The 2nd differences :
3, 3, 3
Since it takes two rounds of differences to arrive at a constant difference between terms, the nth term will be a 2nd degree polynomial of the form: , where c is a constant. The coefficients a, b, and the constant c can be found.
We can form the following 3 equations with 3 unknowns a, b, c:
Solving for a, b, c, we get:
a = 3/2, b = -1/2, c = 0
Therefore, the nth term of the given sequence is: