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Math Help - basic maths

  1. #1
    abi
    abi is offline
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    basic maths

    need help

    word problem
    darren went on holiday.in 5 days he rides his bike 120 miles.each day he rode 6 miles less than the previous day .how many miles did he ride each day ?.if he went on riding his bike 6 miles less each day,how far would he have ride altogether?
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Bikes!

    Let X be the number of miles he rode the first day then

    X+(X-6)+(x-6-6)+(x-6-6-6)+(x-6-6-6-6)=120

    The rest is up to you!
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  3. #3
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    1st day-26

    2nd day-25

    3rd day-24

    4th day-23

    5th day-22
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  4. #4
    -1
    e^(i*pi)'s Avatar
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    Quote Originally Posted by abi View Post
    need help

    word problem
    darren went on holiday.in 5 days he rides his bike 120 miles.each day he rode 6 miles less than the previous day .how many miles did he ride each day ?.if he went on riding his bike 6 miles less each day,how far would he have ride altogether?
    You would get an arithmetic sequence with common difference -6 and first term 120.

    5th day: U_n = a+(n-1)d

    In your case n=5, d=-6, a= 120.

    You can use the recurrent relation for the days in between:

    U_{n+1} = a-(U_n)d with the terms same as above.

    ------

    For the total use the formula for the sum of an arithmetic sequence:

    S_n = \frac{n}{2}(2a+(n-1)d) with the terms the same as above
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