Day: February 3, 2018

Week 1 – My Arithmetic Sequence

by nighinar2016

Arithmetic Sequence 2, 9, 16, 23, 30…

Using these five terms, we are going to solve for  t_{50}, t_{n}, and S_{50}

 

The formula t_{n} = t_{1} + (n – 1)d will help us solve for t_{50}. d stands for the difference which is 7. We then are able to fill the formula in.

t_{n} = t1 + (n – 1)d

t_{50} = 2 + (50 – 1)7

t_{50} = 2 + 49(7)

t_{50} = 2 + 343

t_{50} = 345

 

To find the general form of t_{n} we use the same formula from above and just fill in what we know which is t_{1} and d.

t_{n} = t_{1} + (n – 1)d

t_{n} = 2 + (n – 1)7

Then you distribute the 7.

t_{n} = 2 + 7n – 7

t_{n} = 7n – 5

 

Finding s50 uses the formula \frac{n}{2} (t1 + tn).

s50 = \frac{50}{2} (2 + 345)

s50 = 25(347)

s50 = 8675