Find the missing term in the following numbers series questons.
500,548,620,?,836,980

Options

A. 716
B. 736
C. 756
D. 696

Answer

To find the missing term in the series 500, 548, 620, ?, 836, 980, we will analyze the differences between the consecutive terms and see if we can identify a pattern.

### Step-by-Step Solution:

1. **Identify the given series:**
The series is: 500, 548, 620, ?, 836, 980.

2. **Calculate the differences between consecutive terms:**
- Difference between 548 and 500:
\[ 548 - 500 = 48 \]
- Difference between 620 and 548:
\[ 620 - 548 = 72 \]

3. **Let the missing term be \( x \). Calculate the difference between \( x \) and 620:**
- Difference between \( x \) and 620:
\[ x - 620 \]
- Difference between 836 and \( x \):
\[ 836 - x \]

4. **Calculate the difference between 980 and 836:**
\[ 980 - 836 = 144 \]

5. **Now, we have the differences:**
- From 500 to 548: 48
- From 548 to 620: 72
- From 620 to \( x \): \( x - 620 \)
- From \( x \) to 836: \( 836 - x \)
- From 836 to 980: 144

6. **Observe the pattern in the differences:**
The differences appear to be increasing. Let's analyze the differences we have:
- First difference: 48
- Second difference: 72
- Third difference (from 620 to \( x \)): Let's denote it as \( d_1 = x - 620 \)
- Fourth difference (from \( x \) to 836): Let's denote it as \( d_2 = 836 - x \)
- Fifth difference: 144

7. **Assuming the differences are increasing by a constant amount:**
The difference from 48 to 72 is an increase of 24. If we assume the next difference increases by the same amount (24), we can calculate:
\[ d_1 = 72 + 24 = 96 \]
Therefore, we have:
\[ x - 620 = 96 \implies x = 620 + 96 = 716 \]

8. **Now, calculate \( d_2 \):**
\[ d_2 = 836 - 716 = 120 \]

9. **Verify the last difference:**
The difference from 836 to 980:
\[ 980 - 836 = 144 \]

10. **Final verification of differences:**
- 500 to 548: 48
- 548 to 620: 72
- 620 to 716: 96
- 716 to 836: 120
- 836 to 980: 144

The differences are indeed increasing by 24 each time. Thus, the missing term is:

\[ \boxed{716} \]