TS EAMCET · Maths · Binomial Theorem
The numbers \(a_n=6^n-5 n\) for \(n=1,2,3, \ldots\) when divided by 25 leave the remainder
- A 9
- B 7
- C 3
- D 1
Answer & Solution
Correct Answer
(D) 1
Step-by-step Solution
Detailed explanation
Given, \(a_n=6^n-5 n, n=1,2,3, \ldots\) We take; \(6^n=(1+5)^n\) Expand with binomial expansion \(6^n={ }^n C_0+{ }^n C_1 5+{ }^n C_2 5^2+{ }^n C_3 5^3+\ldots\) \(6^n=1+n \cdot 5+{ }^n C_2 25+{ }^n C_3 5^3+\ldots\)…
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