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In a sequence, each number after the first number is obtained by adding 4 to the previous number. If the first number in the sequence is 7, which of the following expressions represents the nth number in the sequence?

Respuesta :

MrRoyal

Answer:

[tex]T_n = 3+ 4n[/tex]

Step-by-step explanation:

From the question, we understand that:

[tex]T_1 = 7[/tex] ---- First Term

[tex]d = 4[/tex] ---- Common difference

Required

Determine the nth term

nth term of a sequence is calculated using:

[tex]T_n = T_1 + (n - 1)d[/tex]

Substitute values for [tex]T_1[/tex] and [tex]d[/tex]

[tex]T_n = 7 + (n - 1) * 4[/tex]

Open bracket

[tex]T_n = 7 + 4n - 4[/tex]

Collect Like Terms:

[tex]T_n = 7 - 4+ 4n[/tex]

[tex]T_n = 3+ 4n[/tex]

Hence, the nth term of the sequence is:

[tex]T_n = 3+ 4n[/tex]

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