**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

**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

**If T**_{n}= 5 – 4n, find first three terms

Solution:

For n = 1,

T_{1} = 5 – 4×1 = 5 – 4 = 1

For n = 2

T_{2} = 5 – 4×2 = 5 – 8 = – 3

For n = 3

T_{3} = 5 – 4×3 = 5 – 12 = – 7

**If T**_{n}= 2n^{2}+ 5, find (i) T_{3}and T_{10}

Solution:

If ^{ }T_{n} = 2n^{2} + 5 then T_{3} = 2(3)^{2} + 5

= 2(9) + 5

= 18 + 5

= 23

For T_{10} = 2(10)^{2} + 5

= 2(100) + 5

= 200 + 5

= 205

**If T**_{n}= n^{2 }– 1 , find (i) T_{n-1}(ii) T_{n+1}

Solution:

If T_{n} = n^{2 }– 1 then, T_{n-1} = (n – 1)^{2} – 1

= n^{2} – 2n + 1 – 1

= n^{2} – 2n

If T_{n} = n^{2 }– 1 then, T_{n+1} = (n+1)^{2} – 1

= n^{2} + 2n + 1 – 1

= n^{2} + 2n

**If T**_{n}= n^{2}+ 4 and T_{n}= 200, find the value of ‘n’

Solution:

Given, T_{n} = n^{2} + 4 and T_{n} = 200, we have to find the value of n

200 = n^{2}+ 4

200 – 4 = n^{2}

196 = n^{2}

n = 13

**Next exercise – Progressions – Exercise 2.2 – Class X**