Get the free can you tell what the hidden message is mr x

Name : Date : Objective: Students are able to identify the pattern rule for addition as well as subtraction Can you tell what the hidden message is? Help Mr. X to read the complete message by solving

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So now we have one more number pattern, and we will try to solve it so what is the first step yeah first step is finding the differences so now let's do that second term — first term will be 4 minus 1 this will be equal to 3 and third term — second term that is 11 minus 4 this is equal to 7 right, and then we have 29 which is the fourth term — 11 and this gives us 18, and then we have 76 – 29 this will give you 16 – 9 7 + 6 – 2 4 then we have 199 – 76 and this gives us 9 – 6 3 9 – 7 2 & 1 123, so it looks a little complicated series no problem let's see what happens this 3 is actually 3 times 1 which is the first term then we have this 7 this 7 is actually 2 times 4 minus 1 can it be written like this 4 is the second term 2 times 4 minus 1 right and the next difference is 18 it can be written as 2 times 11 that is 22 minus 4 isn't it yes and similarly here we have difference as 47 2 times 29 minus let's try it so 2 times 29 is 2 9 is 18 1 carried forward to 2 so 4 plus 1 5 58 and this is 47 so yes it can be written as 2 times 29 minus 11 right and what about this one 23 here we have 76 so 2 times 76 is two six or twelve one two sevens of 14 plus 115 that is 152 and if we subtract see here we were subtracting 11 which was the previous term of 29 right so if we subtract 29 from 152 let's see what we get 12 minus 9 3 4 minus 2 to 1 123 right, so this can be written as 2 times 76 minus 29 right so now if we see carefully this is what this first is not following any logic but after that if we see the third term minus the second term t3 minus t2 is giving us 2 times T 2 right 2 times t2 minus what is this is the first term right isn't it similarly if we see this carefully this is the fourth term 29 is the fourth term that means t4 — 11 is the third term d3 is giving us two times T 3 – 4 that is the second term right and here if we see we can write T 5 minus T 476 – 29 is 2 times T 4 — x 29 – 11 that is T 3 right similarly this is also T 6 — T 5 is equal to 2 times T 5 minus T 4 right so what logic can be concluded from here if we see these expressions carefully what can we write we can write T n minus T n minus 1 is equal to 2 times T n minus 1 minus T n minus 2 isn't it if you see carefully third term — second term is two times second term — the first one right as we have bound from here we can write t n is equal to this is minus TN minus 1 so if we add TN minus 1 this TN minus 1 will get cancelled and on the right-hand side we will have 3 T n minus 1 minus T n minus 2 right yes but what about the first two terms if you see these two terms they are constant right, so these two terms can be written as it is that is t1 is equal to 1 and T 2 is equal to 4 right so if we assume that these two terms are constant all other terms are following this logic isn't it yes there is one more reason behind these two terms being constant is in calculating the nth term we are referring to previous terms right we are referring n minus first term and n minus second...

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