Sir, Please guide how to solve such questions, i need the thought process and for this question, even solution also ðŸ˜› Question is:
Given that a1, a2, a3…. an is a sequence of real nos satisfying a(n+1) + a(n-1) = 2a(n) + 2^n for n >1. If a1 = 5 and a2 = 13, then a100 = c + 2^d, where c and d are constants. What is the value of c + d?

Find a1, a2, a3. Then check whether there is a pattern for (something) + 2^(someotherthing). Relate the somethings to 1, 2, 3 respectively. You will get an answer. It is a crude version of induction basically….

And no, I’m not going to solve it in detail. No spoonfeeding! (This blog isn’t really the right place for that anyway…)

As I said above, I am not going to solve it ðŸ™‚ Think about that 397 though….are you sure of it? ðŸ˜›

regards
J

Hi J, for lead up 12…tetrahedron question, when we use all 4colors…we can choose in 4c4ways and apply in 1way…so we have only one way….how did u get 2ways for that condition…pls help..

See the previous post https://cat100percentile.com/2015/11/09/cat-15-lead-up-11/ When two sides are painted, then wrt to them the other two sides become distinct. If need be, construct a tetrahedron out of cardboard and convince yourself!

sir why cant we use the partition method here….i.e. for the tetrahedron question if we assume the colours as variables then…a+b+c+d=4, the four is the number of faces….pls help i am little confused….

I am even more confused by your question. The partition method is applicable to distribute distinct objects into identical groups where groups may have multiple objects or may remain empty. NOTHING in that matches with the situation we are discussing here. You can’t mix and match – any random formula to any problem – which is why we have derived each of those formulae to make it clear where they are applicable and where not.

Sir, Please guide how to solve such questions, i need the thought process and for this question, even solution also ðŸ˜› Question is:

Given that a1, a2, a3…. an is a sequence of real nos satisfying a(n+1) + a(n-1) = 2a(n) + 2^n for n >1. If a1 = 5 and a2 = 13, then a100 = c + 2^d, where c and d are constants. What is the value of c + d?

Thanks & Regards

Find a1, a2, a3. Then check whether there is a pattern for (something) + 2^(someotherthing). Relate the somethings to 1, 2, 3 respectively. You will get an answer. It is a crude version of induction basically….

And no, I’m not going to solve it in detail. No spoonfeeding! (This blog isn’t really the right place for that anyway…)

regards

J

Sir, it is more than sufficient, thank you ðŸ™‚

Regards

Is the answer 498? c=397 and d=101

As I said above, I am not going to solve it ðŸ™‚ Think about that 397 though….are you sure of it? ðŸ˜›

regards

J

Hi J, for lead up 12…tetrahedron question, when we use all 4colors…we can choose in 4c4ways and apply in 1way…so we have only one way….how did u get 2ways for that condition…pls help..

See the previous post https://cat100percentile.com/2015/11/09/cat-15-lead-up-11/ When two sides are painted, then wrt to them the other two sides become distinct. If need be, construct a tetrahedron out of cardboard and convince yourself!

regards

J

Awesome J…thanks ðŸ˜Š

sir why cant we use the partition method here….i.e. for the tetrahedron question if we assume the colours as variables then…a+b+c+d=4, the four is the number of faces….pls help i am little confused….

I am even more confused by your question. The partition method is applicable to distribute distinct objects into identical groups where groups may have multiple objects or may remain empty. NOTHING in that matches with the situation we are discussing here. You can’t mix and match – any random formula to any problem – which is why we have derived each of those formulae to make it clear where they are applicable and where not.

regards

J

hi sir

sir can you please explain ..why in the last question we are not multiplying 6 and 4

Or is Plus. Fundamental Principle of Counting.

regards

J