Discrete Math: Prove that 3+3*5+3-5^2+...+3*5^n = (3(5^(n+1) -1))/4

Another Discrete Math and Its Applications problem (Rosen Chapter 5.1 Question 7):
Prove that 3+3*5+3-5^2+...+3*5^n = (3(5^(n+1) -1))/4

Discrete Mathematics and Its Applications playlist:
https://youtube.com/playlist?list=PLm90IN9RVLf_BneWC40564ZZAqpe2sz6-&si=bKhYao84EXCHpl6N

Chapters:
00:00 Introduction
00:56 Base Case P(0)
02:12 Inductive Step
02:38 Induction Hypothesis P(k)
03:20 We Want to Show P(k+1)
04:48 Algebra Steps
10:22 QED and Thanks for Watching

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