TS EAMCET · Maths · Binomial Theorem
For all natural numbers \(n, 3\left(5^{2 n+1}\right)+2^{3 n+1}\) is divisible by
- A 559
- B 17
- C 19
- D 23
Answer & Solution
Correct Answer
(B) 17
Step-by-step Solution
Detailed explanation
\begin{aligned} & 3 \cdot 5^{2 n+1}+2^{3 n+1} \\ & =3 \cdot 5 \cdot 5^{2 n}+2 \cdot 2^{3 n} \\ & =15 \cdot 5^{2 n}+2 \cdot 2^{3 n} \\ & =(17-2) \cdot 25^n+2 \cdot 8^n \\ & =17 \cdot 25^n-2 \cdot 25^n+2 \cdot 8^n \\ & =17.25^n-2\left(25^n-8^n\right) \\ &…
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