Question

What is the nth and the 10th term of this linear sequence
6, 10,14, 18, 22

Answer 1

Explanation:

this linear sequence means : An = an+b

n=1 A1 = a(1)+b=6

n=2 A2=a(2)+b=10

you have the system : a+b=6...(*)

2a+b =10...(**)

from (*) : b=6-a

from (**) : b= 10-2a

10-2a=6-a

-2a+a=6-10

-a=-4

a=4

b=6-a =6-4 = 2

An = 4n+2..... the nth term

the 10th term is :A10 = 4(10)+2=42

other solution : for the nth term

this aritmetic seq when the first term is A1 = 6

the common diference is d= 22-18=18-14=14-10=10-6=4

the nth term is : An =A1+(n-1)d =6+4(n-1) =6+4n-4 =4n+2

Answer 2

`a_(10)` = 42

Explanation:

The n th term I obtained in your previous question, that is

`a_(n)` = 4n + 2

To find the 10 th term substitute n = 10 into the formula

`a_(10)` = 4(10) + 2 = 40 + 2 = 42