Respuesta :

frika

Answer:

[tex]a_n=7n-10[/tex]

Step-by-step explanation:

If [tex]a_1=-3[/tex] and [tex]a_n=a_{n-1}+7,[/tex] then

[tex]a_2=a_1+7=-3+7=4,\\ \\a_3=a_2+7=4+7=11,\\ \\a_4=a_3+7=11+7=18,...[/tex]

So you get the sequence

[tex]-3,\ 4,\ 11,\ 18,\ ...[/tex]

This is the arithmetic sequence with [tex]a_1=-3[/tex] and the difference [tex]d=7.[/tex]

The explicit formula of this sequence is

[tex]a_n=a_1+(n-1)d,\\ \\a_n=-3+(n-1)\cdot7,\\ \\a_n=-3+7n-7,\\ \\a_n=7n-10.[/tex]

remotecontrolbrain

Answer:

[tex]a_n=7n-10[/tex]

Step-by-step explanation:

Without memorizing formulas for arithmetic sequences, it is best to list a first few terms, then realize that a part of each term is proportional to 7n ( a linear function). What remains to determine is the additive term (bias) based on the first value a1:

a1=-3

a2=4

a3=11

a4=18

[tex]a_n=7(n-1)-3=7n-10[/tex]

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