The first term of a series is unity. Every even term is thrice the term preceding it and every odd term is seven times the term preceding it. The sum of the first hundred terms is

The series is 1, 3*1, 7*3*1, 3*7*3*1, 7*3*7*3*1, 3*7*3*7*3*1.........100 terms

The series of the even terms = 3*1, 3*7*3*1, 3*7*3*7*3*1.....

Sum of the first 50 even terms = $$\frac{3(21^{50}-1)}{20}$$

The series of the odd terms = 1, 7*3*1, 7*3*7*3*1.....

Sum of the first 50 even terms = $$\frac{1(21^{50}-1)}{20}$$

Required sum =  $$\frac{3(21^{50}-1)}{20}$$+$$\frac{1(21^{50}-1)}{20}$$

=4*$$\frac{21^{50}-1}{20}$$

=$$\frac{1}{5}(21^{50} - 1)$$

A is the correct answer.