Hello dear learners, Here's the second part of the Arithmetic Progressions. This time, we'll see how to find the *n*th term.

Look at this number pattern.

2, 5, 8, 11, 14, ...

Here, these can be stated as,

T1 = 2

T2 = 5

T3 = 8

T4 = 11

T5 = 14

### The first term of any number pattern is named as 'a'. So in this number pattern, a=2.

T2 means the 2nd term of the pattern.

T3 ----> 3rd term

T4 ----> 4th term

T5 ----> 5th term

.

.

.

Tn ----> *n*th term

*n*th term is an unknown term. We either don't know which term or the value of Tn. Let's find a way to find the *n*th term.

## The formula to find the *n*th term is,

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

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

Tn ----> the unknown term

a ----> the first term of the number pattern

n ----> The term (T7 or T9 or T100 ...)

d ----> common difference

Now all we have to do is to find those information.

In the number pattern,

2, 5, 8, 11, 14, ...

a = 2

d = 5-2 = 3

let's substitute them to the above formulae

Tn = a + (n-1) d

Tn = 2 + (n-1) 3

When simplified,

Tn = 2 + 3n - 3

Tn = 3n-1

So, the formulae of the above number pattern is,

Tn = 3n-1

If we want to find the 6th term of the above pattern, we have to substitute the information to the formulae of the pattern.

Tn = 3n-1

T6 = 3 x 6 -1

T6 = 18 - 1

T6 = 17

**∴** the 6th term is 17.

You can confirm it this way too.

You know that the 5th term is 14 and the common difference is 3. So when we add 3 to the 5th term, we get the 6th term which is 17.

Let's try another number pattern

4, 9, 14, 19, 24, ...

a = 4

d = 9-4 = 5

Let's the formula of this pattern.

Tn = a+(n-1)d

Tn= 4+(n-1)5

Tn = 4 +5n-5

Tn = 5n-1

Let's find the 10th term of this pattern.

Tn = 5n-1

T10 = 5x10 -1

T10 = 50-1

T10 = 49

I think that you understood how to find an unknown term of any number pattern.

Here are some exercises for you.

Find the formula and the 15th term of each of these number patterns.

i) 2, 4, 6, 8, ...

ii) 3, 6, 9, 12, ...

iii) 6, 10, 14, 18, ...

iv) 32, 35, 38, 41,....

v) 10, 13, 16, 19, 22, ....

You are all free to correct me at any point. And also I'm waiting for your feedback and you can support me by giving the answers for the questions above.

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smmtrade (39)4 years agogreat info!

chamudiliyanage (54)4 years agoThanks

kenny-crane (69)4 years agoThis is another very good lesson, teacher! I'll try to get back here if I can and give you some answers. 😎👍

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chamudiliyanage (54)4 years agoThanks ^^ Okay no problem 👍

kenny-crane (69)4 years agoOK now let's do some MATH!!! :D

I'll just do 2 of them, and maybe someone else will come along and want to try the others.

i) Tn = 2n and the 15th term is 30.

iii) Tn = 4n + 2 and the 15th term is 62.

What is my mark, dear teacher? :)

chamudiliyanage (54)4 years agoYeey, dear student, you've scored 2/2! That makes 100% Well done!!!

kaleem345 (60)4 years agoOh nice post shared my friend is good for leaner.....

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chamudiliyanage (54)4 years agoThanks

kaleem345 (60)4 years agoWelcome sweet friend...

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kaleem345 (60)4 years agoThank you like my post, munnah

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yasu24 (69)4 years ago@chamudiliyanageのこと、書いたよ。

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