Which term of the series \( [] 5 3 ,\, [] 5 4 , 1 [] 5 ,\, ...\) is \( √(5) 13 \) ?

The given series is: \[ √(5) ( 1/3, 1/4, 1/5, ). \] Hence, \[ 1 √(5) (3, 4, 5, ) \] are in arithmetic progression (AP). Suppose \( 13 √(5) \) is the \( n th \) term. Then, \[ 13 √(5) = 1 √(5) [ 3 + (n-1) × 1 ] n = 11. \]

Which term of the series \( [] 5 3 ,\, []... - Solved

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Question 17

Mathematics Sequence And Series Hard

Which term of the series \(\frac{\sqrt[]{5}}{3},\, \frac{\sqrt[]{5}}{4},\frac{1}{\sqrt[]{5}},\, ...\) is \(\frac{\sqrt{5}}{13}\) ?

(A) 12

(B) 11

(C) 10

(D) 9

✓ Correct Answer: Option B Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

The given series is: \[ \sqrt{5} \left( \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \ldots \right). \] Hence, \[ \frac{1}{\sqrt{5}}(3, 4, 5, \ldots) \] are in arithmetic progression (AP). Suppose \( \frac{13}{\sqrt{5}} \) is the \( n^{\text{th}} \) term. Then, \[ \frac{13}{\sqrt{5}} = \frac{1}{\sqrt{5}} \left[ 3 + (n-1) \times 1 \right] \Rightarrow n = 11. \]

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