Question

9. In a sequence of numbers, Az = 4,24 = 7 as = 10,06 = 13, a, = 16. Based on this information, which equation can be used to find the nth term in the sequence, un ?

Answer 1

we have

a3=4

a4=7

a5=10

a6=13

a7=16

so

a4-a3=7-4=3

a5-a4=10-7=3

a6=a5=13-10=3

a7-a6=16-13=3

therefore

This is an arithmetic sequence, because the difference between consecutive terms is a constant called common difference d

d=3

the general equation is equal to

`a_n=a_1+d(n-1)`

we have

d=3

so

For n=3

an=4

substitute and solve for a1

`\begin{gathered} 4=a_1+3(3-1) \\ a_1=4-6=-2 \end{gathered}`

the general equation is

`\begin{gathered} a_n=-2+3(n-1) \\ a_n=-2+3n-3 \\ a_n=3n-5 \end{gathered}`

the answer is

an=3n-5