Arithmetic Sequence Q11. Maths textbook standard level

Question

For an arithmetic sequence $U_n$, $U_5 + 2U_3 = U_{12}$. If $U_7 = 25$, find an expression for the general term, $U_n$.

Answer 1

$U_3=a+2d$
$U_5=a+4d$
$U_7=a+6d$
$U_{12}=a+11d$

$U_5+2U_3=U_{12}\implies a+4d+2a+4d=a+11d\implies 2a=3d$

$U_7=a+6d=25 \implies a+2(3d)=25\implies 5a=25$
$\therefore a=5$

Can you calculate $d$ and therefore $U_n$ now?