Hello,

The key to solve these questions is to find the connection between the consecutive terms.First of all the difference between the second and first term is 5-1 =4.

The difference between the third and second terms is 17-5 = 12.

Similarly the difference between the fourth and third terms is 53-17 = 36.

Now look the differences,they follow a different pattern.

4, 12, 36,...

The second term is actually 4 *3.That is 3 times the previous term.Similarly the third term is 3 times the second term (12*3 = 36).So the fourth term will be 3 times the third term 36*3 = 108.

Here 108 is the difference between the fourth and fifth terms of the actual series.Therefore the fifth term of the series will be 53+108 = 161.

Hope this helps!!

Hello,

In the given numerical, 1,5,17,53,.. if we observe the trend then,

• 1
• 1 + ( 1 x 4 ) = 1 + 4 = 5
• 5 + ( 4 x 3 ) = 5 + 12 = 17
• 17 + ( 12 x 3 ) = 17 + 36 = 53

Hence, the next numbers will be,

• 53 + ( 36 x 3 ) = 53 + 108 = 161
• 161 + ( 108 x 3 ) = 161 + 324 = 485
• 485 + ( 324 x 3 ) = 485 + 972 = 1457

Hence, the series will be, 1, 5, 17, 53, 161, 485, 1457,...

Best Wishes.