Which of these sequences are arithmetic?

27, 40, 53, 66, 79

Step-by-step explanation:

This is because all of the numbers share a common difference/change - 13.

The first choice is incorrect as -5 to -3 is adding 2, but -3 to 3 is adding 6, therefore breaking the sequence.

The second choice is incorrect as albeit it add's 1/4 each time, that would be a geometric sequence as it's a common ratio instead.

The third choice is incorrect as it originally adds 7 to each number before suddenly jumping from 28 to 56.

The final choice is incorrect as 1 to 2 is 1 but 2 to 4 is 2, thus, once again, breaking the sequence.

Hope this helps!

x+y = 29, 5x + 2y = 100

step-by-step explanation:

i'm guessing it was a multiple first option was the correct answer

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 ☺