Wiemy, że:

$\{\begin{array}{l}{a}_1+a_5=18\\ a_{30}=a_{14}+12\end{array}$   

$\{\begin{array}{l}{a}_1+a_1+4r=18\\ a_1+29r=a_1+13r+12\end{array}$  

$\{\begin{array}{l}2a_1+4r=18\\ 29r=13r+12\end{array}$

$\{\begin{array}{l}{a}_1+2r=9\\ 16r=12\end{array}$

$\{\begin{array}{l}{a}_1+2r=9\\ r=\frac{12}{16}\end{array}$

$\{\begin{array}{l}{a}_1+2r=9\\ r=\frac{3}{4}\end{array}$

$\{\begin{array}{l}{a}_1+2r=9\\ r=\frac{3}{4}\end{array}$

$\{\begin{array}{l}{a}_1+2\cdot \frac{3}{4}=9\\ r=\frac{3}{4}\end{array}$

$\{\begin{array}{l}{a}_1+\frac{3}{2}=9\\ r=\frac{3}{4}\end{array}$

$\{\begin{array}{l}{a}_1=7\frac{1}{2}\\ r=\frac{3}{4}\end{array}$

 

Odp.: Pierwszy wyraz tego ciągu wynosi 7 ¹/₂, różnica tego ciągu wynosi ³/₄.