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Find the middle term for
Solution:
To get the position value of the middle term, which is also the rth term, consider this formula:
where n is the exponent of a binomial. If n is odd number, then the middle term is only one term and if n is even number, then the middle terms are two terms (consecutively). From the given equation above, if n = 11, then the value of r will be equal to
In this case, we need to get the 6th term of the binomial. To get the value of the rth term of (x + y)n, the formula can be written as
where r > 1. The given formula above must be memorized at all time especially when you are studying about Binomial Theorem. If you don't remember the formula, then you have to use the Pascal's Triangle in order to get the coefficients. Unfortunately, not all people can remember the coefficients of Pascal's Triangle especially if the exponent is high.
Let's go back to the given problem, if n = 11 and r = 6, then the value of the rth term or 6th term will be equal to
