It's 90. See the patterns below:<br />

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2=6 = (2x3) <br />

3=12 = (3x4) <br />

4=20 = (4x5) <br />

5=30 = (5x6) <br />

6=42 = (6x7) <br />

7=56 = (7x8) <br />

8=72 = (8x9) <br />

9=90 = (9x10) <br />

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or <br />

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2= 6 = (2+4)<br />

3=12 = (6+6)<br />

4=20 = (12+8) <br />

5=30 = (20+10)<br />

6=42 = (30+12)<br />

7=56 = (42+14) <br />

8=72 = (56+16)<br />

9=90 = (72+18)<br />

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7=56 & 8=72 are not given, but logic and common knowledge tell us that 7 follows 6, and 8 precedes 9. Our minds automatically supply 7=56 and 8=72 to the sequence to make it logical and come up with 9=90.<br />

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However, there are some who would not supply 7=56 & 8=72 to the sequence and say that: "7 and 8 are not given, don't assume that 7 and 8 are between 6 and 9." So they would skip 7=56 & 8=72 and come up with 9=72 instead of 9=90. They rely on the concrete data given to them.<br />

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People come up with various answers for problems like this one, because we have different ways of seeing patterns, processing data and interpreting information.

The nth term of the sequence is (n+1)(n+2). So if n = 9, the term is 90.

I agree to you but the answer is 56 and not 90..remember this is not series and this problem is proving and yet the no is given base on the fact are..2,3,45,6,9 and if 2=6, 3=12 then what is 9 = 56 which 9 is the 6 on the given so (n+1)(n+2) to satisfy the given nos. some people treat this are series if this is series there is violation in between 6 & 9 coz there is no difference hence any progression can't apply the principle. So then we will prove the given nos base on the given resulting (n+1)(n+2) to satisfy all the given nos.I not good in math but I remember this topic in my Math 105 during my college time..and this question is tricky that's why so many answer 90 but I respect their answer too also..anyhow I just explain why my answer is 9=56 and we prove this no and to satisfy base on the principle of mathematics only..thats the good of mathematics there are laws and principle that could satisfy.

I'm sorry, I could not understand your comments because your English is poor (if English is not your primary language than I sympathize). But I do realize an error. I should have let n = 8, not 9. My intent was to make the first term be associated with the index value n=1. That is, when n=1, A(n) = 6, when n=2, A(n) = 12, etc. Using this definition, A(n) = (n+1)(n+2). So I got that correct. The mistake I made was that the sequence was really indexed by a value m where m = n+1. That is, if n=1, then m=2, and if n=2, then m=3, etc. I said that my solution of 90 was for the case n=9, when really it was for the case m=9, in which case n = m-1 = 8. My answer of 90 was correct yet I quoted the wrong value of n. I should have said this is a function B(m) = m(m+1) so that if m=9, then B(m) = 90. That would have been simpler.

You have to determine if this is an "If, Then" or "Complete/Continue the Pattern" question.<br />

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If you multiply 2 thru 6 by the next number that comes after each of those numbers, you get the total listed...if you multiply 9 by the next number that comes after it(10), you get 90. Some people argue the answer is 72, which is the result of people treating this like a "complete the pattern" problem, rather than an "if, then" problem.<br />

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If your question looks like yours above, I would say 72. Because that looks like "complete/continue the pattern." 2(3)=6; 3(4)=12; 4(5)=20; 5(6)=30; 6(7)=42...it stands to reason that the expectation would be to keep the pattern of having the multiplier increase by 1. If you stick with this, then you have 9(8)=72. Thus completing/continuing the pattern.<br />

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But if it looks like this: "IF: 2=6 3=12 4=20 5=30 6=42 THEN: 9=?," then I would say the answer is 90.

90<br />

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2x 3-x4-x5-x6-x7-x8-x9-x10

I like it when I make ya smile!

I just posted a question similar to yours? waitin for your response.............

90

90 (the left-hand number, in each case given, is multiplied by a number one larger to get the answer on the right side of each equation)

u totally missing the point of being here on ep !!!

90

The number on the left squared plus that number is the number on the right . 9x9=81+9= 90

Really good. That's a third way of solving it I didn't take the time to notice. There's several methods of arriving at the same answers as you see I've posted 2 just recently.

90

9 = 9

x = 6<br />

y = 4<br />

-1= x*-2 + y*-3= -24<br />

0 = x*-2 + y*-3= -24<br />

1 = x*-1 + y*-1= -10<br />

2 = x*1 + y*0 = 6<br />

3 = x*2 + y*0 = 12<br />

4 = x*2 + y*2 = 20<br />

5 = x*3 + y*3 = 30<br />

6 = x*5 + y*3 = 42<br />

7 = x*6 + y*5 = 56<br />

8 = x*6 + y*6 = 60<br />

9 = x*7 + y*6 = 66<br />

10 = x*9 + y*8 = 86ï»¿<br />

<br />

7=511, 8=67, 9=75, And 10=85 And 11=915 the final responseï»¿<br />

<br />

7=40, 8=50 y 9=74 the final responseï»¿<br />

<br />

7=56, 8=70, 9=94, y 10=126 the final responseï»¿<br />

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(the 2 too count).<br />

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3 FINAL RESPONSE I BELIEVE THAN CORRECTS.<br />

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others alternatives:<br />

<br />

7 = 56, 8=64, 9=74, 10=86.<br />

<br />

2=06, 3=12, 4=20, 5=30, 6=42, 7=56, 8=62, 9=70, 10=80, 11=92.<br />

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2=06, 3=12, 4=20, 5=30, 6=42, 7=50, 8=60, 9=72<br />

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if are corrects,the problem is very easy, it isnâ€™t for geniuses

108

Seems pretty simple to most EPer's. But I'll bet if you passed this around the White House, BHO and his economic advisers, working together, don't get it.

63

7=56 8=72 9=90

90

my answer is 90, but I am reading the crazy notions on patterns and see that some way out of the box thinking could come up with the answer 60, figure that pattern of thinking out!

2=6. 3+3=6 so add 6 to last total 3=12. Now 4+4=8...add that to last total=20. 5+5=10...add to last total=30.......9+9=18...add to 42=60

it is not arithmetic,<br />

it is a logistic question.<br />

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the answer is : any value, anything or any answer except 9.

its 54 ! 7 and 8 are not counted because its not concrete statement that its been there. that's logic. <br />

<br />

2*3 = 6<br />

3*4 = 12<br />

4*5 = 20<br />

5*6 = 30<br />

6*9 = 54