Question

What will be the next number in the series:
3, 6, 10.5, 17, 26, ?

• A. 31
• B. 38
• C. 40
• D. 41

Answer 1

The Correct Option is B

The sequence given is: 3, 6, 10.5, 17, 26. To identify the pattern and predict the next number, observe the differences between consecutive terms:

• 6 - 3 = 3
• 10.5 - 6 = 4.5
• 17 - 10.5 = 6.5
• 26 - 17 = 9

Notice that the differences form another series: 3, 4.5, 6.5, 9. The pattern in this series involves an increasing increment:

• 4.5 - 3 = 1.5
• 6.5 - 4.5 = 2
• 9 - 6.5 = 2.5

The increment pattern is increasing by 0.5 each time. Continuing this pattern, the next difference should be 9 + 3 = 12.

So, add this next difference to the last given number in the original series:

• 26 + 12 = 38

Therefore, the next number in the series is 38.

Answer 2

• \(a_2 - a_1 = 6 - 3 = 3\)
• \(a_3 - a_2 = 10.5 - 6 = 4.5\)
• \(a_4 - a_3 = 17 - 10.5 = 6.5\)
• \(a_5 - a_4 = 26 - 17 = 9\)

The differences are: 3, 4.5, 6.5, 9. Now let's find the differences between these consecutive differences:

• \(4.5 - 3 = 1.5\)
• \(6.5 - 4.5 = 2\)
• \(9 - 6.5 = 2.5\)

These differences are: 1.5, 2, 2.5. The difference between these differences is:

• \(2 - 1.5 = 0.5\)
• \(2.5 - 2 = 0.5\)

Since the second difference is constant at 0.5, the next term in the sequence 1.5, 2, 2.5 is \(2.5 + 0.5 = 3\).

So, the next difference in the sequence 3, 4.5, 6.5, 9 is \(9 + 3 = 12\).

Thus, the next term in the series 3, 6, 10.5, 17, 26 is \(26 + 12 = 38\).

Therefore, the next number in the series is 38.