1. The first term of a sequence is 3, the 6th term is 96, find the first 3 terms and the nth term if the sequence is (i) arithmetic, (ii) geometric.

2. (i) Find the AP sequence whose first and 31st terms are 4 and -86, respectively.

(ii) Show that there are two GP sequences whose first and 7th terms are 3/4 and 3/256, respectively.

3. The 8th and 14th terms of the sequence [a+(n-1)d] are -25 and -49, respectively. Find the first term, the common difference and the 20th term.

4. (i) The 3rd and 6th terms of the sequence arn-1 are 40 and 625, show that ar2 = 40 and ar5 = 625, and hence that r = 5/2. Hence find the sequence.

(ii) Show that there are 2 GP sequences whose 2nd and 6th terms are -1/2 and -8/18, respectively. Find the 8th and 9th terms of each sequence.

5. (i) For [a+(n-1)d], the sum of the 3rd and 10th terms is -27, and the sum of the 2nd, 5th and 9th terms is -23. Show that (a+2d)+(a+9d) = -27, and that (a+2d) + (a+9d)= -27 and (a+d)+(a+4d)+(a+8d) = -23. Hence find the sequence and the (r+1)th term.

(ii) For the sum of the 2nd and 3rd terms is -9/4, and the sum of the 4th and 5th terms is -9. Show that and . By dividing, prove that , and that the corresponding values of a are -3/8 and -9/8. Hence find the sequence and the (2n+1)th term.

6. (i) Find the AP sequence un in which and . Also find .

(ii) Find the GP sequence un in which and . Also find .

7. (i) The number 106 is in the nth term of the sequence 4, 7, 10, ..... Show by using the result , that 106 = 4 + (n-1).3 and hence find n.

(ii) The number 2187 is the nth term of the sequence 9, 27, 81, .... Show by using the result that 2187 = 9.(3)n-1 and hence find n.

8. Find the number of terms in each of the following sequences:

(a) (b) (c)

9. (i) For the multiples of 7 between 400 and 600, find F (the first multiple), L (the last multiple) and N (the number of multiples).

(ii) For the set of integers between 330 and 530, which are divisible by 8, find the first and last of these integers, and the number of them.

10. (i) How many multiples of 6 are there between (a) 2 and 200; (b) 200 and 500.

(ii) How many integers divisible by 11, are there in the range (a) 30 to 300; (b) 400 to 600.

11. For the sequence 7, 10, 13, ..... find

(i) the first term greater than 100;

(ii) the last term before 300;

(iii) the number of terms in this range.

12. Find the number of terms of the sequence (i) which lies between 200 and 300. (ii) [13.5, 9, 4.5, .....] which lies between -40 and -50.