Exams › JEE Main › Maths

Given that a1 = 1 and the sequence satisfies aₙ₊₁ = (4 + 3aₙ)/(3 + 2aₙ) for n ≥ 1, if lim_(n→∞) aₙ = a, then the value of a is

1. √2
2. −√2
3. 2
4. None of these

Correct answer: √2

Solution

At the limit a=(4+3a)/(3+2a) gives 2a^2=4, so a=sqrt(2). Since a1=1>0 the sequence stays positive (a2=7/5, ...), converging to the positive root sqrt(2).

Related JEE Main Maths questions

• If Sₙ = cosⁿ θ + sinⁿ θ, then the value of 3S₄ - 2S₆ is
• For a natural number n, the inequality 2^(n - 1) < nⁿ holds when
• For any natural number n, the product n(n + 1) is always
• For which positive integers n does the inequality 3ⁿ exceed n³?
• For which values of n does the inequality 4ⁿ/(n+1) < (2n)!/(n!)² hold, if P(n) denotes this statement?
• For a positive integer n, define a(n) = 1 + 1/2 + 1/3 + 1/4 +... + 1/(2ⁿ - 1). Which of the following is true?

⚔️ Practice JEE Main Maths free + battle 1v1 →