## Sequences and Series

#### Sequences and Series

1. Find out the next term in the series 7, 11, 13, 17, 19, ...

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. 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. (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 = (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. 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