This week in Math 11 we learned about Series and Sequences. Sequence is essentially to just a pattern that starts at a number and continually goes up my the same number each time. And a Series is the sum of all the numbers of the sequence . The one thing that stood out for me and was challenging to learn was figuring out how to find t_1 being given S_n and t_n. After figuring it out, it’s safe to say it’s essentially just figuring out what you don’t know, what you do know, and which equation to use.

Example:

The Work:

Step 1: Figure out what you know and don’t know based on what’s given in the question

In this example, we know t_1 = 5 and t_{25} = 101 and we don’t know what d or t_{30} is equal to or what S_{30} is equal to.

** t_1 is the first number in the sequence the series represents

** t_n or t_3 or any number that is attached to the t is the general term that represents the place of whatever the number is ( t_{15} is the 15th term in the sequence)

** d is the difference between the number add uns in the pattern which has to stay the same throughout to be a artithmetic sequence

Step 2: Find d

Finding D is the most important in this question because before we can find S_{30} we have to find t_{30} and we can’t do that without knowing the difference between each term in the pattern

Step 3: find t_{30}

Finding the 30th term is important too because of its connection to S_{30} which is that for there to be an S_{30} there has to be a 30th term in the sequence that the series can add up until. And to figure out S_{30} we need to know what t_{30} is because we need to know what the number is to add in the series

Step 4: Figure out what you know now and what you still need to know

In this example, now we know at this point that t_1 =5, d = 5, and t_{30} = 121 and we still don’t know what S_{30} is equal to

Step 5: Find S_{30}

At this point, we have all the information we need to use the series equation and find what we were looking for in the beginning