## Sequences and Series

#### Sequences and Series

1. Find out the next term in the series 7, 11, 13, 17, 19, ...
1. 21
2. 23
3. 27
4. None of these

1. Given series is a consecutive prime number series.

##### Correct Option: B

Given series is a consecutive prime number series. Therefore, the next term will be 23.

1. Find the missing term 6, ?, 21, 33, 48
1. 14
2. 20
3. 12
4. 18

1. Series Pattern
+6, +9, +12, +15...

##### Correct Option: C

Series Pattern
+6, +9, +12, +15....
∴ Missing term = 6 + 6 = 12

1. Find the value of the expression 1 - 2 + 3 - 4 + 5 - 6 + 7 + .... upto 100 terms . ?
1. -150
2. -60
3. -100
4. -50

1. (1 - 2) = -1
(3 - 4) = -1
(5 - 6) = -1

##### Correct Option: D

(1 - 2) = -1
(3 - 4) = -1
(5 - 6) = -1
and so on.
∴ Total terms of -1 will be 50.
∴ Answer = -1 x 50 = -50

1. If A represents the arithmetic mean, H represents the harmonic mean and G represents the geometric mean, then what is the relation between them ?
1. A x H = G
2. A x H = G2
3. A/H = G2
4. A/H = G

1. A = (a + b)/2,
1/H = (1/a + 1/b)/2
⇒ H = 2ab/(a +b),
G = √ab

##### Correct Option: B

A = (a + b)/2,
1/H = (1/a + 1/b)/2
⇒ H = 2ab/(a +b),
G = √ab
∴ A x H = {(a + b)/2} x {2ab/(a + b)} = ab = G2
∴ A x H = G2

1. 4, 12, 36, ?, 324, 972
1. 108
2. 125
3. 215
4. 312

1. Series pattern
Every next element = 3 x previous element

##### Correct Option: A

Series pattern
Every next element = 3 x previous element
∴ Missing term = 3 x 36 = 108