Given the series:

$$1, 3, 6, 21, 88, 445, 2676$$

One number in this series is wrong. Consider this wrong number as the value of *A* in the second series defined by the pattern:

$$B = A imes 1 + 1$$
$$C = B imes 2 + 2$$
$$D = C imes 3 + 3$$

Find the value of *D* based on the pattern of the first series.

Question

Given the series:

$$1, 3, 6, 21, 88, 445, 2676$$

One number in this series is wrong. Consider this wrong number as the value of *A* in the second series defined by the pattern:

$$B = A 	imes 1 + 1$$
$$C = B 	imes 2 + 2$$
$$D = C 	imes 3 + 3$$

Find the value of *D* based on the pattern of the first series.

Accepted Answer

**Solution:**

1. The given series is:
   $$1, 3, 6, 21, 88, 445, 2676$$

2. The pattern mentioned is:
   $$	imes 1 + 1, 	imes 2 + 2, 	imes 3 + 3, 	imes 4 + 4, 	imes 5 + 5, 	imes 6 + 6$$

3. Check the series step-by-step:
   - Start with 1
   - Next number: $1 	imes 1 + 1 = 2$ (but given is 3, so 3 is wrong)

4. So, the wrong number is 3. We take $A = 3$ for the second series.

5. Calculate $B$, $C$, and $D$:
   - $B = A 	imes 1 + 1 = 3 	imes 1 + 1 = 4$
   - $C = B 	imes 2 + 2 = 4 	imes 2 + 2 = 10$
   - $D = C 	imes 3 + 3 = 10 	imes 3 + 3 = 33$

**Answer:** $33$

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