How to proof linearity property of summations with induction

Recently I have faced with this question:

${\sum_{k=1}^{n} (ca_k+ b_k) = c \sum_{k=1}^{n} a_k + \sum_{k=1}^{n} b_k }$

Proof linearity property of summations for all n ≥ 0 by using mathematical induction on n

I know that proving with induction is basically trying with $P(1)$, $P(m)$ and $P(m+1)$ however in my previous examples, right hand side always had one simple equation with only n variable. This does not, so I don't know how to solve this. Could someone explain and solve please? I progressed until here, don't know what else to do:

${c \sum_{k=1} ^{m} a_k + \sum_{k=1} ^{m} b_k + ca_{m+1}+ b_{m+1}}$