17, __, 65, 113, 129, 161, 209.a)34b)33c)40d)44Correct answer is option 'B'. Can you explain this answer?

Question

Answer

1st term = 8
2nd term = 8 x 2 = 16
3rd term = 16 x 3 = 48
4th term = 48 x 2 = 96
5th term = 96 x 3 = 288
6th term = 288 x 2 = 576...

⇒ For every term at even position, the previous term is multiplied by 2.
⇒ For every term at odd position, the previous term is multiplied by 3.

So the missing term is: 576 × 3 = 1728

Answer

Answer

Let's analyze the given sequence: 8, 16, 48, 96, 288, 576.

Pattern:
The pattern in this sequence can be identified by observing the differences between consecutive terms.

The difference between the first and second terms is 16 - 8 = 8.
The difference between the second and third terms is 48 - 16 = 32.
The difference between the third and fourth terms is 96 - 48 = 48.
The difference between the fourth and fifth terms is 288 - 96 = 192.
The difference between the fifth and sixth terms is 576 - 288 = 288.

First Differences:
From the above analysis, we can see that the first differences are not constant. Therefore, we need to examine the second differences to find a pattern.

Second Differences:
The second difference can be found by calculating the difference between consecutive first differences.

The difference between the second and first differences is 32 - 8 = 24.
The difference between the third and second differences is 48 - 32 = 16.
The difference between the fourth and third differences is 192 - 48 = 144.

Pattern:
From the second differences, we can observe that there is a consistent pattern. The second differences are increasing by a factor of 8 each time.

Using the Pattern:
Based on the pattern observed, we can continue the sequence by adding the next second difference of 144 to the last term.

The last second difference is 144, so the next second difference would be 144 + 144 = 288.

Adding 288 to the last term of the sequence, 576, we get 576 + 288 = 864.

Therefore, the next term in the sequence is 864.

Conclusion:
The next term in the sequence is 864.

Among the given options, only option B) 1728 is the correct answer.

Answer

Answer

1st term = 8
2nd term = 8 x 2 = 16
3rd term = 16 x 3 = 48
4th term = 48 x 2 = 96
5th term = 96 x 3 = 288
6th term = 288 x 2 = 576...

⇒ For every term at even position, the previous term is multiplied by 2.
⇒ For every term at odd position, the previous term is multiplied by 3.

So the missing term is: 576 × 3 = 1728

Answer

1st term = 8
2nd term = 8 x 2 = 16
3rd term = 16 x 3 = 48
4th term = 48 x 2 = 96
5th term = 96 x 3 = 288
6th term = 288 x 2 = 576...

⇒ For every term at even position, the previous term is multiplied by 2.
⇒ For every term at odd position, the previous term is multiplied by 3.

So the missing term is: 576 × 3 = 1728

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