the even numbers are aranged in groups as follows 2;4,6;8,10,12;14,16,18,20;......... see the details?

Question

the even numbers are aranged in groups as follows 2;4,6;8,10,12;14,16,18,20;......... [a] what is the first number in the nth group? [b] what is the sum of the numbers in the nth group?

Answer 1

First off, let me just say that this is NOT an easy question... it took me awhile before I saw the patterns... so being stuck on this problem is UNDERSTANDABLE!!!

PART A)

n(n+1) + 2 ... if 0 is assigned to "n" to get 2....

n
0 2
1 4 6
2 8 10 12
3 14 16 18 20
4 22 24 26 28 30
5 32 34 36 38 40 42
6 44 46 48 50 52 54 56
7

See the pattern??

There is also another solution...

n(n-1) + 2 ... if 1 is assigned to "n" to get 2

n
0
1 2
2 4 6
3 8 10 12
4 14 16 18 20
5 22 24 26 28 30
6 32 34 36 38 40 42
7 44 46 48 50 52 54 56

It just depends on what "n" you are starting with first....

If you start your "n" with 0 for the 1st group.... then the answer will be... the CURRENT "n" TIMES the NEXT "n" = the first term of your current group "n" series... or n(n+1) + 2

If you start your "n" with 1 for the 1st group... then the answer will be... the CURRENT "n" TIMES the PREVIOUS "n" = the first term of your CURRENT group "n" series... or n(n-1) + 2

PART B)

(n+1)^3 + (n+1) ... if 0 is assigned to "n" to get 2....

n sum
0 2
1 10 next "n" is 2... so... 2^3 + 2 = 8 + 2 = 10
2 30 next "n" is 3.... so... 3^3 + 3 = 27 + 3 = 30
3 68 next "n" is 4.... so.... 4^3 + 4 = 64 + 4 = 68
4 130 next "n" is 5.... so.... 5^3 + 5 = 125 + 5 = 130
5

See the pattern??

There is also another solution...

n^3 + n ... if 1 is assigned to "n" to get 2...

n sum
1 2 = 1^3 + 1
2 10 = 2^3 + 2
3 30 = 3^3 + 3
4 68 = 4^3 + 4
5 130 = 5^3 + 5

See the pattern???

AGAIN, just as in Part A), it just depends on what "n" you are starting with first....

If you start your "n" with 0 for the 1st group.... then the answer will be... the NEXT "n" raised to the 3rd power + the NEXT "n"... or " (n+1)^3 + (n+1) "

... and that's the sum of the numbers in the nth group

BUT.... If you start your "n" with 1 for the 1st group... then the answer will be... the CURRENT "n" raised to the 3rd power + the CURRENT "n"... or " n^3 + n "

... and, if you start your 1st group with n=1, then that's the sum of the numbers in the nth group... the sum woul be " n^3 + n "

Hope this helps!!!

Answer 2

The Red Sox play three with the Blue Jays then fly to Seattle for 4. I will say 4-3 through next Sunday. BQ Hey, Scooter, it's your contest. You can borrow from the BCS and use degree of difficulty as the tiebreaker. If the Cardinals had 3 with the Cubs and 3 with the Padres and the Nationals had 3 with the Dodgers and 3 with the Braves, and both the Cardinals and the Nationals were 4-2 and scored the same number of runs, you would look at the combined record of the opposition and award the points to the Nationals fan, as an example. Hope that helped.

Answer 3

The pattern is like this:
Each value is 2n where n= whole number integers (1,2,3,...,n) Each group has an increasing number of values of n in it that so each set contains (1 number, 2 numbers, 3 numbers,..., n numbers). And the first number in each set is im not sure.
Based on these observations
a) The first number in the nth group is i'm not sure
b)The sum of the values in each set is 2(2n+1). For the first set n=1, the second n=2, etc...