If sum of n terms of a sequence is given by `S _(n) = 2n ^(2) - 4n,` find its `50^(th)` term.

Answer

To find the 50th term of the sequence given the sum of the first n terms \( S_n = 2n^2 - 4n \), we can use the formula for the nth term of a sequence, which is:

\[ T_n = S_n - S_{n-1} \]

### Step 1: Calculate \( S_{50} \)

First, we need to calculate \( S_{50} \):

\[ S_{50} = 2(50)^2 - 4(50) \]

Calculating this gives:

\[ S_{50} = 2(2500) - 200 = 5000 - 200 = 4800 \]

### Step 2: Calculate \( S_{49} \)

Next, we calculate \( S_{49} \):

\[ S_{49} = 2(49)^2 - 4(49) \]

Calculating this gives:

\[ S_{49} = 2(2401) - 196 = 4802 - 196 = 4606 \]

### Step 3: Find \( T_{50} \)

Now we can find the 50th term \( T_{50} \):

\[ T_{50} = S_{50} - S_{49} \]

Substituting the values we calculated:

\[ T_{50} = 4800 - 4606 = 194 \]

### Conclusion

Thus, the 50th term of the sequence is:

\[ \boxed{194} \]