Find the first five terms of the sequence in which a1 = –10 and an = 4an – 1 + 7, if n ≥ 2.

The new sequence

-40, -160, -640, -2560, -10240, -40960

Step-by-step explanation:

It is given that,

aₙ = 4a₍ₙ₋₁₎ and a₁ = -10

To find the first 7 terms of the sequence

a₁ = -10

a₂ = 4a₁ = 4 * (-10) = -40

a₃ = 4a₂ = 4 * (-40) = -160

a₄ = 4a₃ = 4 * ( -160) = -640

a₅ = 4a₄ = 4 * (-640) = -2560

a₆ = 4a₅ = 4 * (-2560) = -10240

a₇ = 4a₆ = 4 * (-10240) = -40960

Therefore the new sequence

-40, -160, -640, -2560, -10240, -40960

Given Below

Step-by-step explanation:

Given

 for n greater than equal to 2

using above equation

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.

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 ☺