General Awareness:-- Reasoning Part 1
TYPE 1 : NUMBER SERIES and Patterns
Case I : Completing the Given Series
(1) Which number would change question mark in the series 7, 12, 19,
The given sequence follows the pattern :
+ 5, +7, +9 ... i.e., 7 + 5 = 12, 12 + 7=19
Missing number = 19 + 9 = 28.
(2) Which is the number that comes after in the sequence :
0. 6. 24. 60. 120. 210 ?
Sol. Clearly, the given series is l³ - 1, 2³ - 2, 3³ - 3, 4³ - 4. 5³ - 5. 6³-6
Next number will be= 73 - 7 = 343 - 7 = 336.
Elementary idea of Progressions s
I. Arithmetic Progression AP series — The progression of the form
a. a + d, a + 2d,a + 3d,... is known as an A.P. with first of the term = a and common difference « d.
Ex. 3, 6, 9, 12, ... is an A.P. with a = 3 and d = 6 - 3= 3.
In an A.P., we have nth term • a + (n - l)d.
II. Geometric Progression GP series — The progression of the form is known as a G.P. with first term comes a and common ratio = r.
Ex. 1, 5, 25, 125, ... is a G.P. with a = 1 and r = 7 = v = ... = 5.
In a Geometric progression series, we have nth term = ar^n-1
Ex. In the series 357, 363, 369, .... what will be the 10th term ?
Sol. The given series is an A.P. in which a = 357 and d =» 6.
10th term will be= a (10 - 1) d = a + 9d.
= (357 • 9 x 6) * (357 * 54) - 411.
How many terms will be there in the series 201, 208, 215, 369 ?
Sol. The given series in an A.P. in which a * 201 and d « 7.
Let the number of terms be n.
So, i.e. 369 = 201 + (n - 1) x 7 or n = 25.
In the series of 7, 14, 28 what will be the 10th term ?
Sol. Clearly. 7 x 2 = 14. 14 x 2 that is 28, ... and so on.
So, the given series is a Geometric progression in which a = 7 and r = 2.
10th term will be =ar^n-1
= ar9 = 7x2^9 = 7x 512 » 3584
Examples...
1) 20, 19, 17, (??), 10, 5
The pattern is - 1, - 2, ...
Missing number = 17 - 3 = 14.
2) Which term of the series 5. 10. .20, 40, ... is 1280 ?
5 x 2 = 10.10 x 2 = 20.20 x 2 - 40,...P
So. the series is a G.P. in which term a - 5 and r = 2.
Let the number of terms be n.
ar^n-1
Then, 5 x 2* ~ 1 = 1280
2* ~1 = 256 = 2*
n - 1 that is= 8 or n = 9.
3) In the series 2. 6. 18. 54. ..., what will be the 8th term ?
2 * 3 = 6. 6 * 3 = 18. 18 * 3 = 54
So. the series is a G.P. in which term a = 2 and r = 3.
.'. 8th term = ar^n-1
= 2*3^(8-1)
=4374
Do it Yourself...
3, 4. 7, 7, next term 13, 13, 21, 22, 31, 44, ( )
(a) 42 (b) 43 (c) 51
2, 6, 12, 20. 30, 42, 56, ( )
(a) 60 (b) 64 (c) 70 (d)72
3. 9. 27. 81. ( )
(a) 324 (b) 243 (c) 210 (d) 162
7. 1. 9. 17. 33. 49. 73. ( )
(a) 97 (b) 98 (c) 99 (d)100
8. 2. 5. 9. ( ), 20. 27
(a) 14 (b) 16 (c) 18 (d) 24
9. 5, 9, 17, 29. 45, ( )
(a) 60 (6) 65 (c) 68 (d) 70
Case I : Completing the Given Series
(1) Which number would change question mark in the series 7, 12, 19,
The given sequence follows the pattern :
+ 5, +7, +9 ... i.e., 7 + 5 = 12, 12 + 7=19
Missing number = 19 + 9 = 28.
(2) Which is the number that comes after in the sequence :
0. 6. 24. 60. 120. 210 ?
Sol. Clearly, the given series is l³ - 1, 2³ - 2, 3³ - 3, 4³ - 4. 5³ - 5. 6³-6
Next number will be= 73 - 7 = 343 - 7 = 336.
Elementary idea of Progressions s
I. Arithmetic Progression AP series — The progression of the form
a. a + d, a + 2d,a + 3d,... is known as an A.P. with first of the term = a and common difference « d.
Ex. 3, 6, 9, 12, ... is an A.P. with a = 3 and d = 6 - 3= 3.
In an A.P., we have nth term • a + (n - l)d.
II. Geometric Progression GP series — The progression of the form is known as a G.P. with first term comes a and common ratio = r.
Ex. 1, 5, 25, 125, ... is a G.P. with a = 1 and r = 7 = v = ... = 5.
In a Geometric progression series, we have nth term = ar^n-1
Ex. In the series 357, 363, 369, .... what will be the 10th term ?
Sol. The given series is an A.P. in which a = 357 and d =» 6.
10th term will be= a (10 - 1) d = a + 9d.
= (357 • 9 x 6) * (357 * 54) - 411.
How many terms will be there in the series 201, 208, 215, 369 ?
Sol. The given series in an A.P. in which a * 201 and d « 7.
Let the number of terms be n.
So, i.e. 369 = 201 + (n - 1) x 7 or n = 25.
In the series of 7, 14, 28 what will be the 10th term ?
Sol. Clearly. 7 x 2 = 14. 14 x 2 that is 28, ... and so on.
So, the given series is a Geometric progression in which a = 7 and r = 2.
10th term will be =ar^n-1
= ar9 = 7x2^9 = 7x 512 » 3584
Examples...
1) 20, 19, 17, (??), 10, 5
The pattern is - 1, - 2, ...
Missing number = 17 - 3 = 14.
2) Which term of the series 5. 10. .20, 40, ... is 1280 ?
5 x 2 = 10.10 x 2 = 20.20 x 2 - 40,...P
So. the series is a G.P. in which term a - 5 and r = 2.
Let the number of terms be n.
ar^n-1
Then, 5 x 2* ~ 1 = 1280
2* ~1 = 256 = 2*
n - 1 that is= 8 or n = 9.
3) In the series 2. 6. 18. 54. ..., what will be the 8th term ?
2 * 3 = 6. 6 * 3 = 18. 18 * 3 = 54
So. the series is a G.P. in which term a = 2 and r = 3.
.'. 8th term = ar^n-1
= 2*3^(8-1)
=4374
Do it Yourself...
3, 4. 7, 7, next term 13, 13, 21, 22, 31, 44, ( )
(a) 42 (b) 43 (c) 51
2, 6, 12, 20. 30, 42, 56, ( )
(a) 60 (b) 64 (c) 70 (d)72
3. 9. 27. 81. ( )
(a) 324 (b) 243 (c) 210 (d) 162
7. 1. 9. 17. 33. 49. 73. ( )
(a) 97 (b) 98 (c) 99 (d)100
8. 2. 5. 9. ( ), 20. 27
(a) 14 (b) 16 (c) 18 (d) 24
9. 5, 9, 17, 29. 45, ( )
(a) 60 (6) 65 (c) 68 (d) 70
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