revision questions

1. Given the function f (x) = x3 + x - 1 = 0, a) Show that the equation has a root in the interval [0,1] [3] b) Use the Newton-Rapson formula to show that Xn+1 = 2xn +1 3xn2+1 [5] c) Hence, find the root to 2 d.p. 19] 2. The sum of the first n terms of a series is given by Sn = 14n - 2n2 a) Find the nth term of the series [5] b) Show that the series is arithmetic [4] c) Find the first term and common difference of the series [4] 3. The third term of an AP is four times the sixth term and the sum of the first ten terms is 150. Find a) The first term and the common difference [4] b) The least number of terms of the Arithmetic Progression which must be taken for the sum to be negative [5] 4. The sum of an infinite GP is 1000 and the common ratio is 0.2 Calculate a) The first term [3] b) The 15th term [3] 5. Find the number of different arrangements of the word PARAMETRIC [3]