Find the missing term in the following numbers series:
1864,1521,1305,?,1116,1089

Options

A. A)1160
B. B)1180
C. C)1095
D. D)1205

Answer

To find the missing term in the number series: 1864, 1521, 1305, ?, 1116, 1089, we will analyze the differences between the consecutive terms and look for a pattern.

### Step 1: Calculate the differences between the terms
1. **First difference**: 1864 - 1521 = 343
2. **Second difference**: 1521 - 1305 = 216
3. **Third difference**: 1305 - ? = ?
4. **Fourth difference**: ? - 1116 = ?
5. **Fifth difference**: 1116 - 1089 = 27

### Step 2: Identify the differences
Now we have the differences:
- 343 (which is \(7^3\))
- 216 (which is \(6^3\))
- ? (missing term)
- ? (missing term)
- 27 (which is \(3^3\))

### Step 3: Determine the missing differences
We can see that the differences seem to follow a pattern of cubes:
- The first difference is \(7^3\)
- The second difference is \(6^3\)
- The third difference should be \(5^3 = 125\)
- The fourth difference is \(4^3 = 64\)
- The last difference is \(3^3 = 27\)

### Step 4: Calculate the missing term
1. From 1305, we subtract \(5^3\) (125):
\[ ? = 1305 - 125 = 1180 \]

2. Now, we can check if this value fits with the next term:
\[ 1180 - 1116 = 64 \quad (which is \, 4^3) \]

### Conclusion
The missing term in the series is **1180**.