Week 1-My Arithmetic Sequence

My arithmetic sequence is 12,15,18,21,24……

Part 1-How to find $t_{50}$ and general equation for $t_n$ ?

Solution:

Know- $t_1$ =12

d=15-12

d=3

$t_n$ = $t_1$ +（n-1）d

$t_n$ =12+(n-1)3

$t_n$ =12+3n-3

$t_n$ =9+3n

$t_{50}$ =9+3(50)

$t_{50}$ =9+150

$t_{50}$ =159

Part 2-How to determine the sum of these first 50 terms?

Solution:

$S_n=\frac{n}{2}(t_1+t_n)$

$S_{50}=\frac{50}{2}(12+159)$

$S_{50}=\frac{50}{2}(171)$

$S_{50}=4275$