Maths-
General
Easy

Question

Write recursive formula and explicit formula. -15,-6,-3,12,21,...

Hint:

  • Recursive Formula is a formula that defines the each term of sequence using the previous/preceding terms.

The correct answer is: a_n=9n-24


    Explanation:
    • We have given a sequence -15,-6,-3,12,21,.....
    • We have to find the recursive and explicit formula of the given sequence.
    Step 1 of 2:
    We have given a sequence -15,-6,-3,12,21,.....
    The given sequence is an AP.
    We know that the recursive formula for any AP is a subscript n equals a subscript n minus 1 end subscript plus d , where d is common difference.
    Here the common difference is 9
    So, The recursive formula is

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals a subscript n minus 1 end subscript plus d end cell row cell a subscript n equals a subscript n minus 1 end subscript plus 9 end cell end table
    Step 2 of 2:
    The given sequence is an AP.
    So, The explicit formula will be

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals negative 15 plus left parenthesis n minus 1 right parenthesis left parenthesis 9 right parenthesis end cell row cell a subscript n equals negative 15 plus 9 n minus 9 end cell row cell a subscript n equals 9 n minus 24 end cell end table

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