Week 2- PRE-Calculas 11

On this week, we have learned about geometric sequence and series. Geometric sequence could be defined as the arranged numbers that have constant common ratio. If you want to get t_n, you can use the formula. –> t_n = t_1  x  r^{n-1}

Geometric Series is sum of all the arranged number of geometric sequence. But the thing is that, there are two kinds of geometric series. They are ‘FINITE GEOMETRIC SERIES” and “INFINITE GEOMETRIC SERIES”. First of all, if you want to get series of finitie geometric series, you can use the formula.

–> s_n =  a ( r^n – 1) / (r-1)

 

If you want to get “INFINITE GEOMETRIC SERIES”, you should observe the common ratio first. If the common ratio is bigger than negative 1, and smaller than positive 1, it has a sum.

formula–> s_{infinite} = t_1 / (r-1)

If the common ratio is bigger than positive 1 or smaller than negative 1, it has no sum.

Week 1 – My Arithmetic Sequence

-9, -4, 1, 6, 11, 16, ———————–(keep going)

To find t_{50}  we should use the formula that has come from the idea of adding or subtracting constant common difference.

–> t_n = t_1 + d(n-1)

We know that t_1 = -9,    common difference= +5

—> t_{50}= -9 + 5(50-1) = -9 + 5 X 49 = 236

 

Then, we need to get the series from term 1 to term 50.

To find s_{50}, we should use the formula that has come up with idea of Carlous Gauss.

–> s_{50} = n/2 ( t_1 + t_{50} )

We know that  t_1  = -9,   t_{50} = 236,   n= 50

——–>  s_{50}  = 50/2 ( -9   +   236 ) =  25 X  227 = 5675

Week1 – Precalc 11

We have learned ‘sequence’ and ‘series’ on the first week of September. Sequence is a kind of collection of numbers that has arranged on a regular difference. The difference between Term 2 and Term 1 is called as ” common difference”. Common difference is also written as “d”. If you want to predict other terms, you should think of the pattern. Let’s think about the basic first. If you want to predict third term, you will have to add two times of ‘d’ with the first term. –> third term is equal to “d+d+the first term”. Then if you want to solve the thirtieth term, then you will make an equation like this –> the first term + 29d. Therefore if you want to predict nth term, then you can make an eqation: the first term + d(n-1).