Find the wrong number in the following number series:

$$251, 252, 254, 227, 243, 118, 154$$

Question

Find the wrong number in the following number series:

$$251, 252, 254, 227, 243, 118, 154$$

Accepted Answer

**Solution:**

1. Observe the series: $$251, 252, 254, 227, 243, 118, 154$$

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

- From 251 to 252: $$+1$$
   - From 252 to 254: $$+2$$
   - From 254 to 227: $$-27$$
   - From 227 to 243: $$+16$$
   - From 243 to 118: $$-125$$
   - From 118 to 154: $$+36$$

3. The differences seem to follow a pattern alternating between cubes of negative integers and squares of positive integers:

- $$-1^3 = -1$$
   - $$+2^2 = +4$$
   - $$-3^3 = -27$$
   - $$+4^2 = +16$$
   - $$-5^3 = -125$$
   - $$+6^2 = +36$$

4. According to this pattern, the first difference should be $$-1$$ (not $$+1$$), which means the second term should be:

$$251 - 1 = 250$$

5. But the given second term is 252, which breaks the pattern.

**Answer:** 252 is the wrong number in the series.

Answer

Answer

Answer

Answer