Explain to me..?

Question

Find an expression in terms of n, for the nth term of the sequence 17, 14, 11, 8, 5, ...

The answer is 20 - 3n

I don't understand why there is a 20 and a 3 in the expression and why a minus sign is present..Could someone explain it to me so that I could resolve my doubts? Thanks!

Answer 1

There is a special term for this type of sequence. It is called an Arithmetic Progression (AP).

It is a sequence of numbers in which the difference between two consecutive terms is the same constant. We call that constant, the common difference and it is denoted by 'd' The first term of an AP is generally denoted by 'a'.

Examples of an AP are:
1, 2, 3, 4, 5, ...
2, 5, 8, 11, 14, ...
0, -3, -6, -9, ...
5, 2, -1, -4, -7, ...
1, 1, 1, 1, 1, ... (Yes, this is also an AP!)

d can be positive or negative, as we have seen. d can also be 0!

Now, if we were to write an AP using notations 'a' and 'd', we would get:

a, a + d, a + 2d, a + 3d, ...

which is the general form of an AP.

There are n terms in an AP. There is a simple formula to find the nth term. nth term is denoted by a(n)

a(n) = a + (n - 1)d

Using, this, we get your answer:

In your AP,
a = 17,
d = -3
a(n) is the nth term

a(n) = a + (n - 1)d
= 17 + (n - 1)(- 3)
= 17 - 3n + 3
= 20 - 3n

Answer 2

Okay...eazy peazy...

it is a decreasing sequence right? Now they want you to come up with a formula so you can work out the nth term or say they want you to find out the 59th term, what do you do?

You look at it and you can see that the terms are reducing gradually by a factor of 3 from it's preceding term, hence the -3.

Okay now, using -3 how can you get the first term? You have to ensure that n=1 in the first term as per definition. So the only way to get 17, or the first term is by the formula 20-3n, so that this will work for each and every term in the decreasing sequence.

Hope it helps.

Answer 3

= 20 - 3(1) = 20 - 3 = 17
= 20 - 3(2) = 20 - 6 = 14
= 20 - 3(3) = 20 - 9 = 11
= 20 - 3(4) = 20 - 12 = 8
= 20 - 3(5) = 20 - 15 = 5

That explains it. The constants are 20 and 3. The n could be any number multiplied by the 3 constant and the product deducted from 20 constant.

Answer 4

well, every number in the sequence is 3 less than the one before it, which is where the three comes in... and 20-3 =17, the first number of the sequence, so with 20-3n, for 14, the second number, you'd have 20-3(2) or 20-6=14 and so on... hope this helps

Answer 5

N may be 1 as 20 - 3(1)= 17 and so on, as 17- 3(1)=14,, like wise subract 3 from the preceeding ones. Since the first one is 17, the no. 20 is there.

Answer 6

the number starts from 17 which is 3 less than 20 and the next number is 14 which is 6 less than 20... the sequence is formed by numbers less than 20 by multiples of 3...

Answer 7

1st term = 17
and decrease by 3 each time

nth term = 17 - 3(n-1)
= 17 - 3n + 3
= 20 -3n

Answer 8

A positive plus a positive equals a negative.