Sequences and Series
- The ninth term of the sequence 0, 3, 8, 15, 24, 35, .... is
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The pattern of following series is given :
0 + 3 = 3
3 + 5 = 8
8 + 7 = 15
15 + 9 = 24
24 + 11 = 35
35 + 13 = 48
........... and so onCorrect Option: C
The pattern of following series is given :
0 + 3 = 3
3 + 5 = 8
8 + 7 = 15
15 + 9 = 24
24 + 11 = 35
35 + 13 = 48
48 + 15 = 63
63 + 17 = 80
Hence , The ninth term of the sequence is 80 .
- (1 + 3 + 5 + 7 + 9 + .... + 99) is equal to
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Expression = 1 + 3 + 5 + ....... + 99 = (1 + 2 + 3 + 4 + ....... + 100) – (2 + 4 + 6 ..... + 100)
Expression = (1 + 2 + 3 + 4 + ....... + 100) – 2(1 + 2 + 3 ..... + 50)Expression = 100(100 + 1) - 2 × 50 (50 + 1) 
∵ 1 + 2 + 3 + .....+ n = n(n + 1) 
2 2 2
Correct Option: B
Expression = 1 + 3 + 5 + ....... + 99 = (1 + 2 + 3 + 4 + ....... + 100) – (2 + 4 + 6 ..... + 100)
Expression = (1 + 2 + 3 + 4 + ....... + 100) – 2(1 + 2 + 3 ..... + 50)Expression = 100(100 + 1) - 2 × 50 (50 + 1) ∵ 1 + 2 + 3 + .....+ n = n(n + 1) 2 2 2
Expression = 50 × 101 – 50 × 51
Expression = 50 (101 – 51) = 50 × 50 = 2500
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The nth term of the sequence 1 , n + 1 , 2n + 1 .......is n n n
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From the given question ,
First term, a = 1 n Common difference, d = n + 1 - 1 = n + 1 - 1 = 1 n n n
∴ nth term = a + (n –1) dnth term = 1 + (n - 1) . 1 n
Correct Option: B
From the given question ,
First term, a = 1 n Common difference, d = n + 1 - 1 = n + 1 - 1 = 1 n n n
∴ nth term = a + (n –1) dnth term = 1 + (n - 1) . 1 n nth term = 1 + n² - n = n² - n + 1 n n
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Which term of the sequence 1 , - 1 , 1 , - 1 ..........is - 1 ? 2 4 8 16 256
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As per the given question ,
The sequence is : 1 , - 1 , 1 , - 1 ,.........- 1 2 2² 2² 24 28
It is a G.P. with common ratio = – 1 / 2
∴ nth term = an = arn – 1⇒ 1 = 1 . 1 - 256 2 ( -2)n - 1
Correct Option: B
As per the given question ,
The sequence is : 1 , - 1 , 1 , - 1 ,.........- 1 2 2² 2² 24 28
It is a G.P. with common ratio = – 1 / 2
∴ nth term = an = arn – 1⇒ 1 = 1 . 1 - 256 2 ( -2)n - 1 ⇒ 1 = 1 -27 ( -2)n - 1
Equating on both sides , we get
⇒ n – 1 = 7 ⇒ n = 8
- The first odd number is 1, the second odd number is 3, the third odd number is 5 and so on. The 200th odd number is
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Here , First odd number = 1
Second odd number = 3
Third odd number = 5
Common difference ( d ) = 3 - 1 = 5 - 3 = 2
∴ nth odd number = 1 + (n – 1) 2 = 2n – 1Correct Option: A
Here , First odd number = 1
Second odd number = 3
Third odd number = 5
Common difference ( d ) = 3 - 1 = 5 - 3 = 2
∴ nth odd number = 1 + (n – 1) 2 = 2n – 1
∴ 200th odd number = 2 × 200 – 1 = 400 – 1 = 399
