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The recursive formula for an arithmetic sequence is given below. What is the fourth term in
the sequence?


A. -30
B. -18
C. -12
D. -24

The recursive formula for an arithmetic sequence is given below What is the fourth term in the sequence A 30 B 18 C 12 D 24 class=

Respuesta :

Hrishii

Answer:

B. -18

Step-by-step explanation:

In order to find the fourth term of the sequence, first find second term, next, third term and finally fourth term.

[tex]a_n = - 6 + a_{(n - 1)} \\ \\ \implies \: a_2 = - 6 + a_{(2 - 1)} = - 6 + a_1 = - 6 + 0 \\ \\ \implies \: \pink{a_2 = - 6} \\ \\\: a_3 = - 6 + a_{(3 - 1)} = - 6 + a_2 = - 6 + ( - 6) \\ \\ \implies \: \purple{ a_3 = - 12}\\ \\\: a_4= - 6 + a_{(4 - 1)} = - 6 + a_3 = - 6 + ( - 12) \\ \\ \implies \: \huge { \red{a_4 = - 18}}[/tex]

Another way:

[tex]a_1=0[/tex]

[tex]a_2=-6[/tex](Calculated above)

[tex]a_3=-6+a_2=-6-6=-12[/tex]

[tex]a_4=-6+a_3=-6-12=-18[/tex]

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