Explanation

a = 3, r = 2

5th term:

3, 6, 12, 24, 48

Explanation

This is a product of fractions:   (4/3)(5/4)(6/5)...(51/50) 

All middle terms cancel:   Only 51/3 = 17

This product simplifies to 17 when all terms from 1/3 to 1/50 are multiplied as shown.

Explanation

6 → ? → 60 → 120 → 12

Maybe pattern between 60 → 120 → 12  

120 is double of 60  

Then 12 is 1/10th of 120  

Looking at options, 12 fits as repeating

Explanation

To determine which sequence is similar to the given sequence 77677: 76767: 77767,

we need to identify the pattern and match it to one of the provided options.

Pattern in the Given Sequence (77677: 76767: 77767):

The first sequence (77677): The digits are primarily "7," with the fourth digit being "6."

Second sequence (76767): The digits are primarily "7," with the third digit being "6."

Third sequence (77767): The digits are all "7" except for the fourth digit, which is "6."

7677: 76767: 77767

First sequence: 7677 (no similarity in length and pattern).

Second sequence: 76767 (similar to the second sequence of the given pattern).

Third sequence: 77767 (similar to the third sequence of the given pattern).

Conclusion:

Option 4 (7677: 76767: 77767) is the sequence most similar to the original sequence 77677: 76767: 77767,

as it maintains the same pattern in the second and third sequences, with the only difference being the length of the first sequence.

Explanation

The digit pattern/order in 677855 is different from the others.

It breaks the common arrangement rule.

Explanation

Let's try to find the consistent difference between numbers:

- 54 → 43 → difference = -11  

- 43 → 34 → difference = -9  

- 34 → 26 → difference = -8  

- 26 → 22 → difference = -4  

- 22 → 19 → difference = -3  

- 19 → 18 → difference = -1

The differences are not follow a regular pattern.

Now assume correct pattern:  

Try subtracting odd numbers in decreasing order:

- 54 - 11 = 43  

- 43 - 9 = 34  

- 34 - 7 = 27  

- 27 - 5 = 22  

- 22 - 3 = 19  

- 19 - 1 = 18

So if the intended pattern was subtracting odd numbers in sequence (11, 9, 7, 5, 3, 1):

The correct sequence should be:  

54, 43, 34, 27, 22, 19, 18

So the number 26 in the original sequence is wrong.  

It should have been 27 instead of 26.

Correct wrong number: 26  

Correct sequence: 54, 43, 34, 27, 22, 19, 18

Explanation

Series pattern is =6+9+12+15

6+6=12 is missing 

Explanation

11 + 8 = 19

19 + 10 = 29

29 + 12 = 41

41 + 14 = 55.

Explanation

Fibonacci sequence: next number is sum of previous two → 8 + 13 = 21

Explanation

 Alternating square pattern: 1², 2², 2², 4², 8² → next is 16² = 256