Answered

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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 ?

9 In A Sequence Of Numbers Az 424 7 As 1006 13 A 16 Based On This Information Which Equation Can Be Used To Find The Nth Term In The Sequence Un class=

Sagot :

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

[tex]a_n=a_1+d(n-1)[/tex]

we have

d=3

so

For n=3

an=4

substitute and solve for a1

[tex]\begin{gathered} 4=a_1+3(3-1) \\ a_1=4-6=-2 \end{gathered}[/tex]

the general equation is

[tex]\begin{gathered} a_n=-2+3(n-1) \\ a_n=-2+3n-3 \\ a_n=3n-5 \end{gathered}[/tex]

the answer is

an=3n-5

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