# Write the terms a 1 </msub> , a 2 </msub> , a

Write the terms ${a}_{1},{a}_{2},{a}_{3},$ and ${a}_{4}$ of the following sequences. If the sequence appears to converge, make a conjecture about its limit. If the sequence diverges, explain why.
${a}_{n+1}=\frac{10}{{a}_{n}};{a}_{1}=1$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Alexis Fields
${a}_{n+1}=\frac{10}{{a}_{n}},{a}_{1}=1$
We have to find ${a}_{2}$

Put $n=1$
${a}_{1+1}=\frac{10}{{a}_{1}}$
${a}_{1+1}=\frac{10}{{a}_{1}}$
${a}_{2}=10$

Put $n=2$
${a}_{2+1}=\frac{10}{{a}_{2}}$
${a}_{3}=\frac{10}{10}$
${a}_{3}=1$

Put $n=3$
${a}_{3+1}=\frac{10}{{a}_{3}}$
${a}_{4}=\frac{10}{1}$
${a}_{4}=10$

Thus, we get the sequence $1,10,1,10,...$
This sequence have two limit points {1,10}. And it is divergence sequence as for convergence sequence should be one limit point.

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee