# Progressions – Exercise 2.1 – Class X

1. Which if the following form a sequence?

(i) 4, 11, 18, 28….

(ii) 43, 32, 21, 10….

(iii) 27, 19, 40 , 70….

(iv) 7, 21, 63, 189…

Solution:

(i) 4, 11, 18, 28…. – forms a sequence

(ii) 43, 32, 21, 10….
10, 21, 32, 43…. – forms a sequence

(iii) 27, 19, 40 , 70…. – not a sequence

(iv) 7, 21, 63, 189… – forms a sequence

1. Write the next two terms of the following sequences

(i) 13, 15, 17, __, ___

(ii) 2/3, 3/4, 4/5, __, ___

(iii) 1, 0.1, 0.01, ___, __

(iv) 6, 1, 24, ___, ___

Solution:

(i) 13, 15, 17, 19, 21

(ii) 2/3, 3/4, 4/5, 5/6, 6/7

(iii) 1, 0.1, 0.01, 0.001, 0.0001

(iv) 6, 12, 24, 48, 96

1. If T­n = 5 – 4n, find first three terms

Solution:

For n = 1,

1 = 5 – 4×1 =  5 – 4 = 1

For n = 2

2 = 5 – 4×2 = 5 – 8 = – 3

For n = 3

3 = 5 – 4×3 = 5 – 12 = – 7

1. If T­n = 2n2 + 5, find (i) T3 and T­10

Solution:

If  n = 2n2 + 5 then T3 = 2(3)2 +  5

= 2(9) + 5

= 18 + 5

= 23

For T10 = 2(10)2 +  5

= 2(100) + 5

= 200 + 5

= 205

1. If Tn = n2 – 1 , find (i) T­n-1 (ii) T­n+1

Solution:

If Tn = n2 – 1 then, T­n-1 = (n – 1)2 – 1

= n2 – 2n + 1 – 1

= n2 – 2n

If Tn = n2 – 1 then, T­n+1 = (n+1)2 – 1

= n2 + 2n + 1 – 1

= n2 + 2n

1. If T­n = n2 + 4 and T­n = 200, find the value of ‘n’

Solution:

Given, T­n = n2 + 4 and T­n = 200, we have to find the value of n

200 = n2+ 4

200 – 4 = n2

196 = n2

n = 13

Next exercise –  Progressions – Exercise 2.2 – Class X