Find the next term of the following
number series :
10, 12, 16, 24, 40, ....

Question

Find the next term of the following
 number series :
 10, 12, 16, 24, 40, ....

Accepted Answer

To determine the next term in the series 10, 12, 16, 24, 40, ..., we need to identify the pattern or rule governing the sequence. Let's analyze the series step by step:

1. **Identify the Pattern:**
   - The first term is 10.
   - The second term is 12. The difference between 12 and 10 is 2.
   - The third term is 16. The difference between 16 and 12 is 4.
   - The fourth term is 24. The difference between 24 and 16 is 8.
   - The fifth term is 40. The difference between 40 and 24 is 16.

Observing the differences: 2, 4, 8, 16, we can see that each difference is a power of 2 (2^1, 2^2, 2^3, 2^4).

2. **Predict the Next Difference:**
   - Following the pattern of powers of 2, the next difference should be 2^5, which is 32.

3. **Calculate the Next Term:**
   - Add this difference to the last term in the series: 40 + 32 = 72.

Therefore, the next term in the series is 72, which corresponds to Option 4.

**Explanation of Incorrect Options:**

- **Option 1 (60):** If we add 20 to the last term (40), we get 60. However, this does not follow the established pattern of increasing differences by powers of 2.

- **Option 2 (56):** Adding 16 to the last term (40) gives 56. This repeats the previous difference rather than following the pattern of increasing powers of 2.

- **Option 3 (70):** Adding 30 to the last term (40) gives 70. This does not align with the pattern of differences being powers of 2.

In conclusion, Option 4 (72) is the correct answer as it follows the logical pattern of the series, where each difference is a power of 2, specifically 2^5 for the next term.