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Finding the nth term of decreasing linear sequences (math help)

Updated on March 14, 2013

Nth Term Of A Decreasing Sequence Video

Finding the nth term of a decreasing linear sequence can by harder to do than increasing sequences, as you have to be confident with your negative numbers.  A decreasing linear sequence is a sequence that goes down by the same amount each time. Make sure that you can find the nth term of an increasing linear sequence before you try decreasing linear sequences. Remember, you are looking for a rule that takes you from the position numbers to the numbers in the sequence!

Example 1

Find the nth term of this decreasing linear sequence.

5              3              1              -1            -3           

First of all write your position numbers (1 to 5) above the sequence (leave a gap between the two rows)

1              2              3              4              5              (1st row)

                                                                                (2nd row)

5              3              1              -1            -3            (3rd row)

Notice that the sequence is going down by 2 each time, so times your position numbers by -2. Put these into the 2nd row.

1              2              3              4              5              (1st row)

-2            -4            -6            -8            -10          (2nd row)

5              3              1              -1            -3            (3rd row)

Now try to work out how you get from the numbers on the 2nd row to the numbers on the 3rd row. Do this by adding on 7.

So to get from the position numbers to the term in the sequence, you have to times the position numbers by -2 and then add on 7.

Hence the nth term = -2n + 7.

Example 2

Find the nth term of this decreasing linear sequence

-9            -13          -17          -21          -25

Again, write your position numbers above the sequence (remember to leave a gap)

1              2              3              4              5              (1st row)

                                                                                (2nd row)

-9            -13          -17          -21          -25          (3rd row)

Notice that the sequence is going down by 4 each time, so times your position numbers by -4. Put these into the 2nd row.

1              2              3              4              5              (1st row)

-4            -8            -12          -16          -20          (2nd row)

-9            -13          -17          -21          -25          (3rd row)

Now try to work out how you get from the numbers on the 2nd row to the numbers on the 3rd row. Do this by taking away 5.

So to get from the position numbers to the term in the sequence, you have to times the position numbers by -4 and then take away 5.

Hence the nth term = -4n - 5.

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  • profile image

    Maxwell 5 years ago

    Try to put chartlfow and graphical representations.That will help understand linear sequences.hanks.

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    nada {eygption} 5 years ago

    i will tell u how to find the 100th term you take your number and times by 99

  • profile image

    elfin 5 years ago

    yuzz...i really need help for a head aching problem of sequence:

    wots the nth term of 54,53,50,43....???????

  • profile image

    Park Min Shin 5 years ago

    Anneyeonghaseyo! I have a test tomorrow wish me luck! :)

    btw the first word was saying "Hello".. Annyeong

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    For cody111 5 years ago

    The answer for that sequence in N squared + 1... because 1x1 (position 1) 1 + 1 = 2... 2(position)x2=4 +1=5.. hope u understand.. luv u! :)

  • profile image

    amy 6 years ago

    lol.

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    cody111 6 years ago

    hello,

    i just needed to know about non-linear equations it,s really confusing.

    please help me on this sequence's nth term:

    2 5 10 17 16

    thanks lots:)

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    Zachman 6 years ago

    Thanks this was helpful!

  • catman3000 profile image
    Author

    Mark 6 years ago from England, UK

    1s term is 12 - 2 x 1 = 12 - 2 = 10

    2nd term is 12 - 2 x 2 = 8

    3rd term is 12 - 2 x 3 = 6

    4th term is 12 - 2 x 4 = 4

    5th term is 12 - 2 x 5 = 2

    So the sequence is 10,8,6,4,2 etc...

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    No-One 6 years ago

    I ready knew this i needed help

    With creating a sequence

    With the nth term as:

    12-2n

  • catman3000 profile image
    Author

    Mark 7 years ago from England, UK

    Hi jay,

    You can use the formula:

    nth term = a + (n-1)d.

    a is the first number in the sequence and d is the common difference of the sequence.

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    jay 7 years ago

    ok but what if u get a queston which says find the formula for a sequence and the numbers are in aposition such as 100th 101th 103rd 104th 105th and so on.

    eg:

    find the formula of this sequence when the 100th is 258 101th is 260 102nd is 262 103rd is 264 104th 266 and 105th is 268th

    good luck

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    ex oh ex oh ;)  7 years ago

    Somebody Helpp me pleaseeeee :) xxxxxxxxxxxxxxxxxxxx

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    nokaa :) xx 7 years ago

    Thaanxxxxxxx a lot for the information, i didn't get it !!!

    oh lala, hola, ge no sE* jo.!!