Sequences and Series
- The next number of the sequence 0, 3, 8, 15, 24, 35, ... is :
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The series is based on following pattern :
0 + 3 = 3
3 + 5 = 8
8 + 7 = 15
15 + 9 = 24
24 + 11 = 35
35 + 13 = ?Correct Option: C
The series is based on following pattern :
0 + 3 = 3
3 + 5 = 8
8 + 7 = 15
15 + 9 = 24
24 + 11 = 35
35 + 13 = ?
⇒ ? = 48
Therefore, the required answer is 48.
- The wrong number of the sequence 4, 9, 25, 49, 121, 144 is
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The pattern of the sequence is :
2² = 4
3² = 9
5² = 25
7² = 49
11² = 121
13² = 169 ≠ 144Correct Option: A
The pattern of the sequence is :
2² = 4
3² = 9
5² = 25
7² = 49
11² = 121
13² = 169 ≠ 144
From above it is clear that these numbers are squares of first 6 consecutive prime numbers. Hence, 144 should be replaced by 169.
The wrong number of the sequence is 144.
- If 1 × 2 × 3 × ...... × n is denoted by n! ,then (8! – 7! – 6!) is equal to :
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As we now that , n! = 1 × 2 × 3 × .........× n
∴ 8! - 7! -6! = (8 × 7 × 6!)– (7 × 6!) – 6!
Required answer = 56 . 6! – 7 . 6! – 6!
Required answer = (56 – 7 – 1) 6!Correct Option: A
As we now that , n! = 1 × 2 × 3 × .........× n
∴ 8! - 7! -6! = (8 × 7 × 6!)– (7 × 6!) – 6!
Required answer = 56 . 6! – 7 . 6! – 6!
Required answer = (56 – 7 – 1) 6!
Hence , Required answer = 48 . 6! = 6 × 8 × 6!
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The 12th term of the series 1 + x + 1 + 2x + 1 + ....... x x x
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As per the given question ,
First term = x × 0 + 1 x First term = x [1 - 1] + 1 x Second term = x × 1 + 1 x Second term = x (2 - 1) + 1 x Third term = x × 2 + 1 x Third term = x(3 - 1) + 1 x ∴ 12th term = x(12 - 1) + 1 x
Correct Option: A
As per the given question ,
First term = x × 0 + 1 x First term = x [1 - 1] + 1 x Second term = x × 1 + 1 x Second term = x (2 - 1) + 1 x Third term = x × 2 + 1 x Third term = x(3 - 1) + 1 x ∴ 12th term = x(12 - 1) + 1 x Hence , 12th term = 11x + 1 x
- The first term of an Arithmetic Progression is 22 and the last term is – 11. If the sum is 66, the number of terms in the sequenceis
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Let Number of terms = n
First term (a) = 22
Last term (L) = –11
Sum (S) = 66∴ S = n (a + L) 2 ⇒ 66 = n (22 - 11) 2 ⇒ 66 = 11n 2
⇒ 11n = 66 × 2
Correct Option: B
Let Number of terms = n
First term (a) = 22
Last term (L) = –11
Sum (S) = 66∴ S = n (a + L) 2 ⇒ 66 = n (22 - 11) 2 ⇒ 66 = 11n 2
⇒ 11n = 66 × 2⇒ n = 66 × 2 = 12 11
