Question

Let {𝑎𝑛 }𝑛≥1 be a sequence such that 𝑎1=1 and 4𝑎𝑛+1=$\sqrt{45 + 16𝑎_𝑛} ,𝑛$=1, 2, 3, … . Then, which one of the following statements is TRUE?

• A. {𝑎𝑛 }𝑛≥1 is monotonically increasing and converges to $\frac{17}{8}$
• B. {𝑎𝑛 }𝑛≥1 is monotonically increasing and converges to $\frac{9}{4}$
• C. {𝑎𝑛 }𝑛≥11 is bounded above by $\frac{17}{8}$
• D. $∑^∞ _ {n=1} a_n$ is convergent

Answer 1

Answer: (B)

{𝑎𝑛 }𝑛≥1 is monotonically increasing and converges to $\frac{9}{4}$

Answer 2

The correct option is (B): {𝑎𝑛 }𝑛≥1 is monotonically increasing and converges to $\frac{9}{4}$