- 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