Series Completion

Clearly, the given the series is moving on the pattern of, 5² + 1² = 26, 5² + 2² = 29, 5² + 3² = 34, 5² + 4² = 41, 5² + 5² = 50, and so on.
So, the next term is 5² + 6² = 61.

Clearly, 1³ - 1² = 0, 2³ - 2² = 4, 3³ - 3² = 18, 4³ - 4² = 48, 5³ – 5² = 100, and so on.
So, the missing term = 6³ - 6² = 180

There are two series (6, 13, 20, 27) and (5, 35, 245, ?), one increasing by 7 and the other multiplied by 7.
So, the next term of series is = 245 x 7 = 1715.

This number series is moving on the pattern of 3¹, 4², 5³, 6⁴, 7⁵, and so on. 
So, the next term of series is 8⁶ = 262144.

There are two series: (5, 8, 11, 14, ?) and (6, 3, 0, -3). The first is increasing by 3 and the second is decreasing by -3, respectively. So, the next term of the series is 14 + 3 = 17.

On multiplying the given numbers by even numbers 2, 4, 6, 8, 10 and so on.
So, the correct next number is 1920 x 12 = 23040.

It is clear that the pattern of the series is,
1 x 1.5 = 1.5, 2 x 2.5 = 5, 3 x 3.5 = 10.5, 4 x 4.5 = 18, 5 x 5.5 = 27.5, and so on.
But 30 = 6 x 5.
It should be 6 x 6.5 = 39

Clearly, the given pattern of this series is 3/7 + ¾  = 33/28, 33/28 + ¾  = 54/28, 54/28 + ¾  = 75/28, 75/28 + ¾  = 96/28, and so on.
So, the next term of the series is: 96/28 + ¾  = 117/28.

The given pattern of this number series is: (1¹ - 1) = 0, (2² - 1) = 3, (3³ - 1) = 26, (4⁴ - 1) = 255, (5⁵ - 1) = 3124, (6⁶ - 1) = 46655 and so on.
So, the next term of the series is (7⁷ - 1) = 823542.

The given pattern of the series is, 7 – 1 + 5 = 11, 11 – 2 + 5 = 14, 14 – 3 + 5 = 16, 16 – 4 + 5 = 17, 17 – 5 + 5 = 17, 17 – 6 + 5 = 16 and so on.
So, the next term is 16 – 7 + 5 = 14.

It is observable that the given pattern of this number series is the product of two consecutive prime numbers starting from 11,
i.e. 11 x 13 = 143, 13 x 17 = 221, 17 x 19 = 323, 19 x 23 = 437, 23 x 29 = 667 and so on.
Therefore, the next term of the series is 29 x 31 = 899.

The given pattern of this series is: 5 is multiplied by consecutive prime numbers starting from 2,
i.e. 5 x 2 = 10, 5 x 3 = 15, 5 x 5 = 25, 5 x 7 = 35, 5 x 11 = 55, 5 x 13 = 65, and so on.
Therefore, the next term is 5 x 17 = 85.

The pattern of the given number series is: 1² x 10 = 10, 2² x 9 = 36, 3² x 8 = 72, 4² x 7 = 112, 5² x 6 = 150, and so on.
So, the next term is 6² x 5 = 180.

Given pattern is +2, -4, +2, -4 and so on.
That means, 10 + 2 = 12, 12 – 4 = 8, 8 + 2 = 10, 10 – 4 = 6, and so on.
So, missing term = 6 + 2 = 8.

It is clear that the given pattern of the series is:
16 x 2 + 2 = 34
34 x 2 – 2 = 66
66 x 2 + 2 = 134
134 x 2 – 2 = 266 and so on.
But 530 = 266 x 2 - 2
It should be 266 x 2 + 2 = 534.