karush said:
The formula for finding the nth term of a binomial expansion is (a+b)^n = nCr(a^n)(b^(n-r)), where n is the power, r is the term number, and a and b are the coefficients. In this case, a = 2x and b = 7.
In this case, r = 5 because we are looking for the 5th term. This number will change for different terms, so make sure to double check which term you are looking for.
Yes, you can use a calculator to find the 5th term. You will need to use the formula mentioned in question 1 and input the values for a, b, n, and r. Make sure to use parentheses to avoid any calculation errors.
The coefficient of the 5th term is the number in front of the variable. In this case, the coefficient is (8C5)(2^3)(7^3) = 56(8)(343) = 153664.
Yes, there is a shortcut method called the Pascal's Triangle method. This method involves finding the corresponding row in the Pascal's Triangle for the power of the binomial, in this case, the 8th row. The numbers in this row represent the coefficients for each term, and the 5th term would be the 5th number in this row, which is 153664.