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8 May, 09:28

Constructing arithmetic sequences Learn Recursive formulas for arithmetic sequences (Opens a modal) Recursive formulas for arithmetic sequences (Opens a modal) Explicit formulas for arithmetic sequences (Opens a modal) Explicit formulas for arithmetic sequences (Opens a modal) Arithmetic sequence problem (Opens a modal) Converting recursive

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  1. 8 May, 12:43
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    Step-by-step explanation:

    To Find:

    recursive form for AS. Explicit form for AS. Arithmetic Sequence problem.

    Solution:

    Recursive form:

    Not all certain can defined in terms of recursive format.

    In this form each term depends upon the preceding term.

    It is formulated by starting term a and depends upon before term An-1.

    It is like ladder structure

    a2=a1+"step up".

    Recursive formula as,

    F (n) = F (n-1) + d ... d is refered as the step up in the arithmetic sequence.

    E. g. 10, 15, 20, 25 ...

    step up is 5 units

    hence for third term is,

    a3=a2+5=15+5=20.

    hence proved by formula in recursive form.

    Explicit Form:

    This form will creates a sequence using n, and number term at that location.

    i. e. It is formulated as the 1st and (one less than term number * common difference).

    F (n) = F (1) + d (n-1).

    for same above example

    f (3) = 10+5 (3-1) = 10+5 (2) = 10+10=20.

    hence proved same result using two different formula.

    Arithmetic sequence problem:

    consider as sequence:

    -6, - 1, 4,?.

    here common difference as

    -1 - (-6) = 5,4 - (-1) = 5.

    hence d=5.

    F (4) = F (1) + d (4-1).

    = - 6+5 (3) = - 6 + 15 = 9.

    The next term is 9 using explicit formula

    now by recursive form

    a4=a3+5=4+5=9

    The 4th term is 9.

    Hence in both forms term being same as "9".

    Depending upon the sequence chose proper method to solve sequences.
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