# Use of inductive reasoning to decide the next 2 numbers....

Use inductive reasoning to find a pattern, and then make a reasonable conjecture for the next number in the sequence. 11 12 9 10 7 8 5 6 ____

Solution Summary

Looking at the given series we can realize that every alternate number is........The complete explanation is given here how I got to the answer.

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Vikas Madan, MCA (IP)

Rating 4.9/5

Active since 2009

BSc, Delhi University
MCA (IP), Indira Gandhi National Open University

Responses 199

Comments on Vikas's work:

"I'm trying to understand JAVA can you please put some comments in every line to help me understand a little bit Thank you!"

"Thanks so much! Your explanations are clear and understandable. Wish you were the instructor!"

"Thanks so much! The instructor has me very confused! There were four questions tied to these contacts. I've typed since I could not copy the instructor's explanation. I am out in left field. Imagine that every single person in your contact list has the same number of people in their contact list as you. Write this total number of all contacts in all the phones (ignore the fact that some may repeat) as an exponential. Next evaluate this exponential. This is what the instructor wrote: This problem is not clear enough at least for two reasons: Total number of all the contacts, N, in all the phones, as it has be stated by course developer, simply means the sum of all the items, X, in all the contact lists, X, whereas contacts, generally , means connecting one on one, or one on two fashion, or anything else for people in all contact lists. If N is the sum of items in all the contact lists then it is not the exponential function, instead it is a power function: N = X * X = X^2. To write it as an exponential function, means to represent it as N = e^X where X = InN is not the independent variable as it should be if the function is Exponential one. It seems like the Course Developer has confused a Power Function and an Exponential Function? Total number of all the contacts N if it is considered as different kinds of communications not as a trivial sum of all the items, might be found on the base of combinaturics rules as a sum of all the possible components. Generally Speaking, the problem is not formulated clearly that is why there are two ways to solve it. 1. Imagine that every single person in your contact list has the same number of people in their contact list as you. Write this total number of all the contacts in all the phones (ignore the fact that some may repeat) as an exponential. Next, evaluate this exponential. 2. Express the value you calculated in the first problem using scientific notation. 3. What would happen if each person added an extra contact. By what percentage would this change your answer? Would this percentage be smaller, larger or the same if someone started with a shorter list? 4. The exponential in number 1 and the value it comes out to can be written as an equality. Rewrite this equality using a logarithm."

"Thank you very much this was very helpful"

"Thanks I truly appreciate your help! One question though please explain the isPrime function and why you used square root and how did that help determine whether a number is prime"