If  a_1=6a1=6  and  a_n=a_{n-1}+3an=an−1+3  then find the value of  a_4a4

The value of

Step-by-step explanation:

Given that and

Given sequence is of the form arithmetic sequence

For arithmetic sequence the sequence is

The nth term is of the form  

Here   and

from this the common differnce is 3.

Therefore d=3

To find  , ,

put n=2 and d=3 we get

  (here   )

Therefore

put n=3 and d=3 we get

  (here   )

Therefore

put n=4 and d=3 we get

  (here   )

Therefore

Therefore the sequence is 6,9,12,15,...

Therefore the value of

step-by-step explanation:

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 ☺