Identify the incorrect term in the following series:

$$19, 23, 32, 48, 73, 109, 154$$

Question

Identify the incorrect term in the following series:

$$19, 23, 32, 48, 73, 109, 154$$

Accepted Answer

**Solution:**

1. Let's analyze the differences between consecutive terms:

- $23 - 19 = 4$
   - $32 - 23 = 9$
   - $48 - 32 = 16$
   - $73 - 48 = 25$
   - $109 - 73 = 36$
   - $154 - 109 = 45$

2. The differences should ideally follow a pattern of perfect squares:

- $4 = 2^2$
   - $9 = 3^2$
   - $16 = 4^2$
   - $25 = 5^2$
   - $36 = 6^2$
   - $45$ is not a perfect square (expected $7^2 = 49$)

3. The last difference should be $49$ instead of $45$, so the last term should be:

$$109 + 49 = 158$$

4. Since the last term given is $154$, which is incorrect, the wrong term in the series is **154**.

**Answer:** $154$

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