There are some series given below and each series contains one wrong term. Find out the wrong term from the series:

100, 240, 480, 1344, 4300.8, 15482.88, 61931.52

Question

There are some series given below and each series contains one wrong term. Find out the wrong term from the series:

100, 240, 480, 1344, 4300.8, 15482.88, 61931.52

Accepted Answer

**Solution:**

1. Given series: 100, 240, 480, 1344, 4300.8, 15482.88, 61931.52

2. Let's analyze the pattern by checking the ratio between consecutive terms:

- $\frac{240}{100} = 2.4$

- $\frac{480}{240} = 2$

- $\frac{1344}{480} = 2.8$

- $\frac{4300.8}{1344} \approx 3.2$

- $\frac{15482.88}{4300.8} = 3.6$

- $\frac{61931.52}{15482.88} = 4$

3. The ratios are: 2.4, 2, 2.8, 3.2, 3.6, 4 — no clear consistent pattern.

4. Try to find a pattern in multipliers. Let's check if the multipliers follow an arithmetic progression:

- If we consider the multipliers as: 2.4, 2, 2.8, 3.2, 3.6, 4

- They are irregular, so check if the third term (1344) is correct.

5. Let's try to find a consistent multiplier pattern starting from 100:

- Suppose the multiplier sequence increases by 0.4 starting from 2.4:

- 1st multiplier: 2.4

- 2nd multiplier: 2.8

- 3rd multiplier: 3.2

- 4th multiplier: 3.6

- 5th multiplier: 4.0

6. Calculate terms using this multiplier pattern:

- Term 1: 100 (given)

- Term 2: $100 	imes 2.4 = 240$ (matches given)

- Term 3: $240 	imes 2.8 = 672$ (given is 480, so 480 is incorrect)

- Term 4: $672 	imes 3.2 = 2150.4$ (given is 1344, so 1344 is incorrect)

7. Since 480 and 1344 both don't fit, check which one fits better with the rest of the series.

8. Calculate next terms using corrected term 3 = 672:

- Term 4: $672 	imes 3.2 = 2150.4$

- Term 5: $2150.4 	imes 3.6 = 7741.44$

- Term 6: $7741.44 	imes 4 = 30965.76$

9. Given terms after 1344 are 4300.8, 15482.88, 61931.52, which are roughly double the calculated values.

10. This suggests the error is at term 4 (1344), which should be 2150.4 to maintain a consistent multiplier pattern increasing by 0.4 starting from 2.4.

**Answer:** 1344

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