If a1 = 1 and an+1 = (4+3an/3+2an), n ge 1 and if displaystyle limn→∞ an = n, then the value of a is

Question

If a1 = 1 and an+1 = (4+3an/3+2an), n ge 1 and if displaystyle limn→∞ an = n, then the value of a is (A) √2 (B) -√2 (C) 2 (D) None of these

Tardigrade Admin · Accepted Answer

We have an+1 = (4+3an/3+2an) ⇒ displaystyle limn→∞ an+1 = lim n→ ∞ (4+3an/3+2an) ⇒ a = (4+3an/3+2an) ⇒ 2a2 = 4 ⇒ a = √2 a ≠ √2 because each an > 0, therefore lim an = a > 0.

Q. If $a_{1} = 1$ and $a_{n + 1} = \frac{4 + 3 a _{n}}{3 + 2 a _{n}}, n \geq 1$ and if $n \to \infty lim a_{n} = n$ , then the value of a is

$2$

$- 2$

$2$

None of these

Q. If a1​=1 and an+1​=3+2an​4+3an​​,n≥1 and if n→∞lim​an​=n, then the value of a is

2​

−2​

2

None of these

We have an+1​=3+2an​4+3an​​⇒n→∞lim​an+1​=n→∞lim​3+2an​4+3an​​ ⇒a=3+2an​4+3an​​⇒2a2=4⇒a=2​ a=2​ because each an​>0, therefore liman​=a>0.

Q. If $a_{1} = 1$ and $a_{n + 1} = \frac{4 + 3 a _{n}}{3 + 2 a _{n}}, n \geq 1$ and if $n \to \infty lim a_{n} = n$ , then the value of a is

$2$

$- 2$

$2$