(15 Points) Indicate the general rule for the arithmetic sequence with a3 = -4 and a8 = -29.

Question

(15 Points) Indicate the general rule for the arithmetic sequence with a3 = -4 and a8 = -29.

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Yến Oanh 2 weeks 2021-07-21T21:34:06+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-07-21T21:35:25+00:00

    Answer:

    General rule » -5n+11

    Step-by-step explanation:

    a3 = a+2d = -4 …….(1)

    a8=a+7d = -29……….(2)

    (2)-(1) » 5d= -25

    d = -25/5

    . = -5

    substitute d = -5 in ( 1)

    » a-2×-5= -4

    a-10 = -4

    a = -4 +10

    = 6

    General rule » a +(n-1)d

    » 6 +(n-1)×-5

    » 6-5n+5

    » -5n+11

    0
    2021-07-21T21:35:39+00:00

    Step-by-step explanation:

    a_3 = – 4

    a_3 = a* + (3- 1) d*

    – 4 = a + 2d . . . . . . . . .(i)

    a_8 = – 29

    a_8 = a + ( 8 – 1) d

    – 29 = a + 7d . . . . . . . . (ii)

    subtracting equations (i) and (ii)

    25 = 5d

    d = -5

    placing d = -5 in equation (i)

    a – 10 = -4

    a = 6

    For an arithmetic Progtession

    a_n = a + (n – 1)d

    a_n = 6 + (n- 1)-5

    a_n = 6 – 5n + 5

     \underline {a_n = 11 - 5n }

    \\

    * \boxed{ \mathfrak { a \:stands\: for\: first\: term  } }

    * \boxed{ \mathfrak { d \:stands\: for\: common \: difference }  }

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