Coding Pattern & Series Quiz-1

Solution:

You are required to define the pattern in the series in variables.

Here 1 is the first term, the next term is 2 till the 3^rd term, 3 till the 6^th term, 4 till the 10^th term, n till the n(n+1)/2 th term.

Thus, 210^th term will be = 20 as (20 × 21)/2 = 210.

So, 300^th term = 24, because (24 × 25)/2 = 300.

The next 25 terms will be 25. So, the required answer is 25.

Answer is 12. Each number is repeated or firstly 0 is added to each number and then 14 is subtracted from it.

Explanation:

Alphabets and their positions

Given number series are 9 8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1 7 6 5 4 3 2 1

• Now the number series becomes  (9 8 7 6 5 4 3 2 1),  (8 7 6 5 4 3 2 1),  (7 6 5 4 3 2 1),...


• From the above series we have that the first term is 9 and in next series the first term is 8 (ie., 9-1=8)


• From the above series we have that in second series its first term is 8 and in next third series its first term is 7 (ie., 8-1=7)

We have the terms of the given series formed in the following manner

⇒ 504 = 8³ – 8

⇒ ? = 9³ – 9

⇒ 990 = 10³ – 10

⇒ 1320 = 11³ – 11

⇒ 1716 = 12³ – 12

Hence, ? = 729 – 9 = 720

The series is

8*3=24; 24/2=12;

12*3=36; 36/2=18;

18*3=54; 54/2=27;

7776,625,64,9,2,

--> 6^{5}=7776

--> 5^{4}=625

--> 4^{3}=64

--> 3^{2}=9

--> 2^{1}=2

--> 1^{0}=1

(3+1=4; 4+2=6; 6+3=9; 9+4=13; 13+5=18)