Which letter-cluster will complete the given series?
FPW, FFPPPWW, FFFFPPPPPWWW, _________

The correct option is FFFFFFFFPPPPPPPWWWW.

To find the missing letter-cluster that completes the series, let us analyze the pattern of each letter (F, P, and W) in the given terms:
1. First term: FPW
2. Second term: FFPPPWW
3. Third term: FFFFPPPPPWWW

Let us count the number of occurrences of each letter in each term:

Count of F:
- 1st term: 1 ('F')
- 2nd term: 2 ('FF')
- 3rd term: 4 ('FFFF')
Here, the number of F's is doubling in each successive term: $1\to 2\to 4$. Following this geometric progression, the 4th term should have:
$4\times 2=8$ F's (FFFFFFFF).

Count of P:
- 1st term: 1 ('P')
- 2nd term: 3 ('PPP')
- 3rd term: 5 ('PPPPP')
Here, the number of P's increases by 2 in each term (consecutive odd numbers): $1\to 3\to 5$. Following this arithmetic progression, the 4th term should have:
$5+2=7$ P's (PPPPPPP).

Count of W:
- 1st term: 1 ('W')
- 2nd term: 2 ('WW')
- 3rd term: 3 ('WWW')
Here, the number of W's increases by 1 in each term (consecutive natural numbers): $1\to 2\to 3$. Following this pattern, the 4th term should have:
$3+1=4$ W's (WWWW).

Combining these counts, the next term in the series must have 8 F's, 7 P's, and 4 W's:
FFFFFFFFPPPPPPPWWWW