Maths-
General
Easy

Question

Write an explicit formula for the arithmetic sequence. a subscript n equals a subscript n minus 1 end subscript minus 3 semicolon a subscript 1 equals 10

Hint:

  • A sequence is said to be arithmetic if the common difference is always constant.
  • The General formula of any AP is a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d.

The correct answer is: a_n =13-3n


    Explanation:
    • We have given an = an - 1 - 3 and a1 = 10
    • We have to find the explicit formula for this AP.
    Step 1 of 1:
    We know that the common difference d is also equal to d equals a subscript n minus a subscript n minus 1 end subscript
    Now in given question we have a subscript n equals a subscript n minus 1 end subscript minus 3
    Ie,

    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 minus a subscript n minus 1 end subscript equals negative 3 end cell row cell d equals negative 3 end cell end table

    And a1 = 10
    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 a subscript 1 plus left parenthesis n minus 1 right parenthesis d end cell row cell a subscript n equals 10 plus left parenthesis n minus 1 right parenthesis left parenthesis negative 3 right parenthesis end cell row cell a subscript n equals 10 minus 3 n plus 3 end cell row cell a subscript n equals 13 minus 3 n end cell end table

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