How can we easily identify which step will solve which question? How can we know which is the formula used to solve in each question? It is so confusing between arithmetic sequence and geometric sequence and arithmetic series and geometric series. PLEASE can you give me some ideas to cope up with the confusion.
Asked by HARI
23rd March 2017,
8:39 PM
Answered by Expert
Answer:
Hello Hari,
I will help you out here. Don't worry.
A progression of the form, a, a+d, a+2d, .... is an Arithmetic Sequence.
So, to understand this you need to find the between two consecutive terms and check if that is equal. If it is equal, then the sequence is an Arithmetic Sequence.
If a progression is of the form, a, ar, ar2, ar3, ...., and when you take the ratio of a term in the progression to its preceeding term for every other term is equal, that is, if they have a common ratio, then the sequence is a Geometric Progression.
Now you should learn the Sum of and AP and a GP, and practise problems of different types on each of these topics.
That will help you, and will reduce your confusion the more you practise.
That will help you, and will reduce your confusion the more you practise.
Once you are clear with these, you will understand that Arithmetic Series is simply the Sum of the terms of an Arithmetic progression.
Example: If the AP is 3, 5, 7, 9, 11
The common difference that is, 5- 3 = 7 - 5 = 9 - 7= 11 - 9
Clearly, there is a common difference between the terms which is = 2.
The arithmetic series is 3+5+7+9+11
Similarly, the sum of the terms of a geometric progression is called a geometric series.
Example: 2, 4, 8, 16, 32 is a GP
Clearly, this is a geometric progression with a common ratio is 2.
Now if you want to master this chapter, I suggest you learn all the formulas. Write the formulas without looking on a sheet and then check if you are right. Then, practise different types of problems based on each type. Think of a way to use these formulas. That is the key to this chapter. I hope this clears your confusion. Do get back to us if you are still confused. Also, if you want to throw in some examples of the type of problems from this chapter you are confused with, do let us know. Thank you.
Answered by Expert
23rd March 2017,
9:28 PM
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