Question

5,19,61,187,565,....​

Answer 1

The given series:

5, 19, 61, 187 ,565, ......​

We have to find, the value of next number(?).

Solution:

The pattern follow:

× 3 + 4.

19 = 5 × 3 + 4

    = 15 + 4 = 19

61 = 19 × 3 + 4

    = 57 + 4 = 61

187 = 61 × 3 + 4

    = 183 + 4 = 187

565 = 187 × 3 + 4

    = 561 + 4 = 565

Similarly,

? = 565 × 3 + 4

⇒ ? = 1695 + 4

⇒ ? = 1699

∴ Next number(?) = 1699

Thus, the value of next number(?) is "equal to 1699".

   

Answer 2

Given:

The series, 5, 19, 61, 187 ,565, ......​

To find:

The value of the next term of the series

Solution:

From given, we have the data as follows.

The series, 5, 19, 61, 187 ,565, ......​

The series is developed using the following pattern :

19 = 5 × 3 + 4  = 15 + 4 = 19

61 = 19 × 3 + 4  = 57 + 4 = 61

187 = 61 × 3 + 4  = 183 + 4 = 187

565 = 187 × 3 + 4  = 561 + 4 = 565

Let 'x' be the next term of the series.

Similarly,

x = 565 × 3 + 4

⇒ x = 1695 + 4

⇒ x = 1699

∴ The next term is, 1699

Thus, the value of the next term in the series is 1699.