(Solved): maths please solve using iteration In each of 3-15 a sequence is defined recursively. Use iteration ...

In each of 3-15 a sequence is defined recursively. Use iteration to guess an explicit formula for the sequence. Use the formulas from Section 5.2 to simplify your answers whenever possible. 3. $a_k=k{a}_{k?1}$, for all integers $k?1$ $a_0=1$ 4. $b_k=\frac{b_{k?1}}{1+b_{k?1}}$, for all integers $k?1$ $b_0=1$ 5. $c_k=3c_{k?1}+1$, for all integers $k?2$ $c_1=1$ 6. $d_k=2d_{k?1}+3$, for all integers $k?2$ $d_t=2$ 7. $e_k=4e_{k?1}+5$, for all integers $k?1$ $e_0=2$ 8. $f_k=f_{k?1}+2^k$, for all integers $k?2$ $f_1=1$ 9. $g_k=\frac{g_{k?1}}{g_{k?1}+2}$, for all integers $k?2$ $g_1=i$ 10. $\begin{array}{l}{h}_k=2^k?h_{k?1},\text{ for all integers }k?1\\ h_0=1\end{array}$ 11. $\begin{array}{l}{p}_k=p_{k?1}+2?3^k\\ p_1=2\end{array}$ 12. $\begin{array}{l}{s}_k=s_{k?1}+2k,\text{ for all integers }k?1\\ s_0=3\end{array}$