Explanation

Decoding the definition of the sequence tells you that, to find the value of each term, you take the previous term, and raise it to the power of the term before it. You know

\(S_{3}=10^2=100\) and \(S_{4}=100^{10}=10^{20}\) and \(S_{5}=(10^{20})^{100}=10^{2000}\).

So \(S_{4}\) is the digit 1 followed by twenty zeroes, which is a total of 21 digits, and \(S_{5}\) is the digit 1 followed by 2,000 zeroes, for a total of 2,001 digits. So the fourth term is the one that meets the condition set forth in the question, and the answer is choice (D).

Sir, in the question the term S3 = 102, but here in this explanation you have written as S3 = 10 ^ 2 = 100. As this confusion occurs for me, I'm unable to move to the next step. Please help me with this explanation

S4 = 100^10 = 10^20
S5 = (10^20)^100 = 10^2000

S5 will have 2000 zeros and a 1, hence 2001 digits.

Hence n = 4, Option D.

S1 = 2

S2 = 10

Sn = (Sn-1)^(Sn-2)

S3 = 100

S4 = 10^20

S5 = 10^2000 = (2000 zeros and 1 so 2001 digits)

Answer n = 4 D

D