How many differents pairs(m, n)can be formed using numbers from the list of whole numbers {1,2,3,320} such that m

Complete question :

How many different pairs (m, n) can be formed using numbers from the list of whole numbers { 1, 2, 3, ..., 20 } such that m < n and m + n is even?

90

Step-by-step explanation:

Given :

Condition :

m < n ; m + n = even number

Thus ;

m = 1 ; n = 3, 5, 7, 9, 11, 13, 15, 17, 19 = 9

m = 2; n = 4, 6, 8, 10, 12, 14, 16, 18, 20 = 9

m = 3 ; n = 5, 7, 9, 11, 13, 15, 17, 19 = 8

m = 4 ; n = 6, 8, 10, 12, 14, 16, 18, 20 = 8

m = 5 ; n = 7, 9, 11, 13, 15, 17, 19 = 7

m = 6 ; n = 8, 10, 12, 14, 16, 18, 20 = 7

Observing the trend :

For ;

m = 7, number of ways = 6

m = 8, number of ways = 6

m = 9, number of ways = 5

m = 10, number of ways = 5

m = 11, number of ways = 4

m = 12, number of ways = 4

m = 13, number of ways = 3

m = 14, number of ways = 3

m = 15, number of ways = 2

m = 16, number of ways = 2

m = 17, number of ways = 1

m = 18, number of ways = 1

m = 19, Number of ways = 0

Hence,

(9+9+8+8+7+7+6+6+5+5+4+4+3+3+2+2+1+1) =90

Hence, we have 90 (m, n) pairs

the answer is su.k.my? ? co.kc

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺