Maths-
General
Easy

Question

Write an explicit formula for the arithmetic sequence.
a subscript n equals a subscript n minus 1 end subscript plus 2.4 semicolon a subscript 1 equals negative 1

hintHint:

  • 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 = 2.4n - 3.4


    Explanation:
    • We have given a subscript n equals a subscript n minus 1 end subscript plus 2.4 and a subscript 1 equals negative 1
    • 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 plus 2.4
    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 2.4 end cell row cell d equals 2.4 end cell end table

    And a1 = -1
    So, The explicit formula will be

    a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d
    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 1 plus left parenthesis n minus 1 right parenthesis left parenthesis 2.4 right parenthesis end cell row cell a subscript n equals negative 1 plus 2.4 n minus 2.4 end cell row cell a subscript n equals 2.4 n minus 3.4 end cell end table

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