contestada

Consider the arithmetic sequence presented in the table below. What is the first term, a1, and the 22nd term of the sequence?
n 5 71
an 42 636

Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference.

Respuesta :

Edufirst
[tex] a_{5}=42=\ \textgreater \ a_{5} = a_{1} +(5-1)d=42 a_{71} =636=\ \textgreater \ a_{71}=a_{1}+(71-1)d=636 [/tex]


Subtract the frist equation from the second equation:

=> 70d - 4d = 636 - 42

66d = 514

=> d = 514 / 66 = 9

Now, find the first term, [tex] a_{1} [/tex]

[tex] a_{1} =42-4d=42-4(9)=42-36=6[/tex]

And the 22nd term is:

[tex] a_{22} = a_{1} +d(22-1)=6+9(21)=6+189=195[/tex]

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