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

## 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 (1^{st}
row)

(2^{nd} row)

5 3 1 -1 -3 (3^{rd}
row)

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

1 2 3 4 5 (1^{st}
row)

-2 -4 -6 -8 -10 (2^{nd}
row)

5 3 1 -1 -3 (3^{rd}
row)

Now try to work out how you get from the numbers on the 2^{nd}
row to the numbers on the 3^{rd} 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 (1^{st}
row)

(2^{nd}
row)

-9 -13 -17 -21 -25 (3^{rd}
row)

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

1 2 3 4 5 (1^{st}
row)

-4 -8 -12 -16 -20 (2^{nd}
row)

-9 -13 -17 -21 -25 (3^{rd}
row)

Now try to work out how you get from the numbers on the 2^{nd}
row to the numbers on the 3^{rd} 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.

## More by this Author

- 26
A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple...

- 0
The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of the faces. A triangular prism has 5 faces, 3 being rectangular and...

- 0
The density, mass and volume triangle is as follows: So if you wanted to work out the density, you would cover up density in the magic triangle to give: Density = Mass/Volume (since mass is above volume) So if...

## Comments 14 comments

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

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

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

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

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

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

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! :)

lol.

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:)

Thanks this was helpful!

I ready knew this i needed help

With creating a sequence

With the nth term as:

12-2n

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

Somebody Helpp me pleaseeeee :) xxxxxxxxxxxxxxxxxxxx

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

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

14