Exercise 2.4: Sequences

Exercise 2.4

1. Find the next three terms of the following sequence.

(i) 8, 24, 72, … (ii) 5, 1,-3, … (iii) 1/ 4, 2/9, 3/16, …

2. Find the first four terms of the sequences whose nth terms are given by

(i) an = n3 âˆ’ 2 (ii) an = (−1)n +1n(n + 1) (iii) an = 2n2 âˆ’ 6

3. Find the nth term of the following sequences

 (i) 2, 5,10, 17,...  (ii) 0, 1/2 , 2/3 ,...  (iii) 3, 8,13, 18,...

4. Find the indicated terms of the sequences whose nth terms are given by

 (i) an = ; a6 and a13

(ii) an = −(n2 âˆ’4); a4 and a11

5. Find a8 and a15 whose n th term is an = 

6. If a1 = 1, a2 = 1 and a n = 2 an−1 +a n âˆ’2, n â‰¥ 3, n âˆˆ N, then find the first six terms of the sequence

Answers:

1.(i) 216,648,1944 (ii) -7 ,-11 ,-15 (iii) 4/25, 5/36 , 6/49

2.(i) -1 ,6,25,62 (ii) 2,-6 ,12,-20 (iii) -4 , 2, 12, 26

3.(i) n2 + 1 (ii) (n-1) / n (iii) 5n - 2

4.(i) 13/3, 15/4 (ii)-12 ,117

5. 63/11, 225/31

6. 1,1,3,7,17,41