A certain arithmetic sequence has this explicit formula for the nth term: an = 12 + (n – 1)(5) The same sequence has this recurs

Question

A certain arithmetic sequence has this explicit formula for the nth term:
an = 12 + (n – 1)(5)
The same sequence has this recursive formula:
an = an-1
+
What number belongs in the blank space in the recursive formula?
A. 5
B. 12
о
C. 17
D. 4

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Khải Quang 3 years 2021-08-08T10:49:56+00:00 1 Answers 96 views 0

Answers ( )

  1. trungdung22
    0
    2021-08-08T10:51:46+00:00
    Reply

    Answer:

    A. 5

    Step-by-step explanation:

    I assume the definitions are

    an = 12 + (n-1)×5

    an = an-1 + blank

    if this is correct, then we have

    a1 = 12

    a2 = 12 + 5 = 17 = a1 + 5

    a3 = 12 + 2×5 = 22 = a2 + 5

    a4 = 12 + 3×5 = 27 = a3 + 5

    …

    we see, for an we need to add (n-1) times the number 5 to the initial a1 value.

    so every new sequence number is larger by 5 than the previous one.

    hence the answer.

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