Day: September 10, 2018

Week 1 – My arithmetic sequence

mitchellw2016 on

Part 1

Find the common difference to this arithmetic sequence, then find t_{50} and the t_{n} equation.

1, -4, 16, -64, 256, -1024, …

t_{n} = t_{1} + (n-1) d

t_{n} = 1 + (50-1) -4

t_{n} = 1+ (-196)

t_{n} = -195

Part 2

The common difference is a multiplecation of -4 when starting at 1.

S_{n} = \frac{n}{2} (t_{1} + t_{2})

S_{50} = \frac{50}{2} [1+ (-195)]

S_{50} = \frac{50}{2} [-194]

S_{50} = 25 [-194]

S_{50} = -4850