Find the wrong term in the given series:

10, 4.5, 3.5, 5, 16, 122, 1904

Question

Find the wrong term in the given series:

10, 4.5, 3.5, 5, 16, 122, 1904

Accepted Answer

**Solution:**

1. Given series: 10, 4.5, 3.5, 5, 16, 122, 1904

2. Let's analyze the pattern between terms:

- From 10 to 4.5: Multiply by 0.5 and subtract 0.5
     $$10 	imes 0.5 - 0.5 = 5 - 0.5 = 4.5$$

- From 4.5 to 3.5: Multiply by 1 and subtract 1
     $$4.5 	imes 1 - 1 = 4.5 - 1 = 3.5$$

- From 3.5 to 5: Multiply by 2 and subtract 2
     $$3.5 	imes 2 - 2 = 7 - 2 = 5$$

- From 5 to 16: Multiply by 4 and subtract 4
     $$5 	imes 4 - 4 = 20 - 4 = 16$$

- From 16 to next term: Multiply by 8 and subtract 8
     $$16 	imes 8 - 8 = 128 - 8 = 120$$

- From 120 to next term: Multiply by 16 and subtract 16
     $$120 	imes 16 - 16 = 1920 - 16 = 1904$$

3. The actual term after 16 should be 120, but the series has 122.

4. Therefore, **122** is the wrong term in the series.

**Answer:** 122

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