Explanation:

Let’s break down the sequence: 2, 3, 6, 10, 17, 28, ?

What stands out is how the jump between numbers grows:

- 3-2 = 1

- 6-3 = 3

- 10-6 = 4

- 17-10 = 7

- 28-17 = 11

Look at those differences: 1, 3, 4, 7, 11. Let's see where this pattern goes:

- 1 ? 3 (add 2)

- 3 ? 4 (add 1)

- 4 ? 7 (add 3)

- 7 ? 11 (add 4)

Those “difference between differences” go: 2, 1, 3, 4. It looks like there’s a repeating pattern emerging: 2, 1, 3, 4.

So, the next difference should be 7 + 4 = 11, then 11 + 2 = 13 (if the pattern repeats).

But the differences between terms are: 1, 3, 4, 7, 11. After 11, the next jump should be 18? Let’s check with the options.

Option 1: 45

? 28 + 17 = 45. Doesn’t fit—17 isn’t in our pattern, unless we adjusted wrong.

Option 2: 39

? 28 + 11 = 39. The last difference was 11, but that’s what we just did.

Option 3: 43

? 28 + 15 = 43. 15 doesn’t fit our difference sequence.

Option 4: 46

? 28 + 18 = 46. 18? The jump from 11 to 18 is an increase of 7, and the difference jumps are 1, 3, 4, 7, 11, so the next logical step is 7 + 11 = 18. Now that clicks.

Correct Answer:

Option 4: 46

Basically, the sequence is building on the sum of the last two “differences.” That’s why the jump goes 7, 11, then 18, and 28 + 18 = 46. So, 46 is what goes in the blank—always satisfying when a pattern clicks together.