Question: 2,6,18,54,_,_

Posted by: Anu P. on 11.07.2022

Hello, Anu! Please check the image for the solution. Hope it helps :)

2*3=6 6*3=18 18*3=54 54*3=162

(2*2)+2= 6, (6*2)+6=18, (18*2)+18=54, (54*2)+54= 162

2*3= 6 6*3= 18 18*3= 54 54*3=162 162*3= 486.. Hence the pattern 2,6,18,54,162,486.....( each digit is multiple of 3 of the preceding digit).
The former number is multiplied by 3 to get the latter number. So the series is 2,6,18,54,162,486,1458.....

2*3=6,6*3=18,18*3=54,54*3=162,162*3=486.....

2*2+2=6

6*2+6=18

18*2+18=54

54*2+54=162

It's a Geometric Progression.. In this as we observe common ratio r is 3. So when.. 2×3=6 6×3=18 18×3=54 54×3=162 162×3=486 and so on..

Ans, 162, 486

Solution : It's a GP, where common ratio r = 6/2 = 3 .

Thus, the required numbers are 54x3 = 162 and 162x3 = 486 and so on ...

2,6,18,54,......... 2×3,6×3,18×3,54×3,162×3 ........
In this question just observe the pattern. S it can be clearly seen that we are getting every subsequent term by multiplying the previous term by 3. Eg. 2*3=6 similarly 6*3=18 18*3=54 Likewise 54*3=162 1

geometric sequence (also known as a geometric progression) is a sequence of numbers in which the ratio of consecutive terms is always the same.

For example, in the geometric sequence 22, 66, 18, 54, 162, …, the ratio is always 33. This is called the common ratio.

If the first term of the sequence is aa and the common ratio is rr, then the geometric sequence can be written as

a, ar, ar2, ar3, …, arn−1, …a, ar, ar2, ar3, …, arn−1, …

which has nth term arn−1

162 2*3= 6, 6*3=18,18*3=54,54*3=162......

2×3=6,6×3=18,18×3=54,54×3=162,162×3=486
54*3=162 and 162*3=486 so 2,6,18,54,162,486......
2,6,18,54,162... 2 x 3= 6 2 x 9 = 18 2 x 27 = 54 2x 81 = 162

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