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Mathematics · JEE | SEQUENCES AND SERIES

हिन्दी

The Fibonacci sequence is defined by \( a_1 = a_2 = 1 \) and \( a_n = a_{n-2} + a_{n-1} \) for \( n > 2 \). What is the value of \( a_5 \)?

  1. A
    5
  2. B
    3
  3. C
    8
  4. D
    13
View Answer & Solution

Correct answer · Option A

5

Explanation

Computing terms: \( a_1 = 1, a_2 = 1, a_3 = 2, a_4 = 3, a_5 = 5 \).

Related questions

Consider the following statements about Geometric Progressions: (I) A sequence \( a_1, a_2, a_3, \dots, a_n, \dots \) is a G.P. if each term is non-zero and \( \frac{a_{k+1}}{a_k} = r \) (constant) for \( k \ge 1 \). (II) The \( n^{\text{th}} \) term of a G.P. with first term \( a \) and common ratio \( r \) is \( ar^{n-1} \). (III) The geometric mean of two positive numbers \( a \) and \( b \) is \( \frac{a+b}{2} \). How many of the above statements are correct?→The sum of some terms of a G.P. is \( 315 \) whose first term and the common ratio are \( 5 \) and \( 2 \), respectively. Find the number of terms.→Match List-I with List-II: List-I List-II A Common ratio of \( 2, 2\sqrt{2}, 4, \dots \) I \( \frac{1}{3} \) B Common ratio of \( \sqrt{7}, \sqrt{21}, 3\sqrt{7}, \dots \) II \( \sqrt{3} \) C Common ratio of \( \frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \dots \) III \( \sqrt{2} \) D Sum of infinite G.P. \( 1 + \frac{1}{2} + \frac{1}{4} + \dots \) IV 2 Choose the correct answer from the options given below:→What is the \( n^{\text{th}} \) term of the sequence defined by \( a_n = \frac{n-3}{4} \)?→
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