Maths-
General
Easy

Question

Casey opened a saving account with a $50 deposit. For every month after the first month she deposits $25. Write an explicit rule to represent the amount of money being deposited in her account. How much money will Casey have in her account after 24 months?

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=625.


    Explanation:
    • We have given Casey opened a saving account with $50 deposit. For every month after the first month she deposits $25.
    • We have to find the explicit rule to represent the amount of money and total amount after 24 months.
    Step 1 of 2:
    In the first month $50 deposited and after that every month $25 will deposits.
    So, This will form an AP.
    So, The explicit form 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 50 plus left parenthesis n minus 1 right parenthesis 25 end cell row cell a subscript n equals 25 plus 25 n end cell end table
    Step 2 of 2:
    After 24 months the amount 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 25 plus 25 n end cell row cell a subscript n equals 25 plus 25 left parenthesis 24 right parenthesis end cell row cell a subscript n equals 25 plus 600 end cell row cell a subscript n equals 625. end cell end table

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