Answer:
a) The sequence is 22 , 28 , 34, 40 ,46 , …..
![a_{n} = 6n +16](https://tex.z-dn.net/?f=a_%7Bn%7D%20%20%3D%206n%20%2B16)
b) The 14 term of the sequence has 100 seats
Step-by-step explanation:
In an auditorium, there are 22 seats in the first row and 28 seats in the second row,...
The sequence is 22 , 28 , 34, 40 ,46 , …..
we observe that the difference between 28 and 22 is '6'
between 34 and 28 is '6'
between 40 and 34 is '6' and so on
The given sequence is <u>arithmetic progression</u>
Here d = 6 , a= 22
The 'n' th term of the sequence ![a_{n} = a +(n-1) d](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%20a%20%2B%28n-1%29%20d)
![a_{n} = 22 +(n-1) 6](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%2022%20%2B%28n-1%29%206)
![a_{n} = 22 +6n-6 = 6n +16](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%2022%20%2B6n-6%20%3D%206n%20%2B16)
b) Given
and find n =?
![100 = a +(n-1) d](https://tex.z-dn.net/?f=100%20%3D%20a%20%2B%28n-1%29%20d)
![22 + (n-1)6 = 100](https://tex.z-dn.net/?f=22%20%2B%20%28n-1%296%20%3D%20100)
![6n-6 = 100-22](https://tex.z-dn.net/?f=6n-6%20%3D%20100-22)
![6n = 78 +6 =84](https://tex.z-dn.net/?f=6n%20%3D%2078%20%2B6%20%3D84)
n = 14
The 14 t h row has 100 seats
<u>Verification</u>:-
substitute n = 14 , a=22 and d=6
![a_{n} = 22 +(14-1) 6 = 100 seats](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%2022%20%2B%2814-1%29%206%20%3D%20100%20seats)