Binomial Theorem – Practice Questions

1.  In the expansion of a3bn , the sum of 9th and 10th term is zero. Find the value of  ab in terms of  n .

2.  If the coefficient of 4th, 5th and 6th terms in the expansion of  1+xn are in arithmetic sequence, then find the value(s) of n .

3.  If the last term in the expansion of  3  13n is log281234 , find the value of  n .

4.  Find the remainder when  21003 is divided by 7. (Non Calculator question)

5.  If  xnyn2=12n  , then show that

       a.  xn22yn2=1n

6. (i) Find the first three terms in the expansion, in ascending powers of x , of 12x5 . [2 marks]

(ii) Given that the coefficient of x2 in the expansion of 1+ax+2x212x5  is 12, find the value of the constant a . [ 3 marks]

7. a) Use the binomial theorem to expand  a+b4
b) Hence, deduce an expression in terms of  a and  b for a+b4+ab4

Q8. Write down and simplify the general term in the binomial expansion of 2x2dx37 , where  d is a constant.
(b) Given that the coefficient of 1x is −70 000, find the value of d .