Hello dear learners, Here's the second part of the Arithmetic Progressions. This time, we'll see how to find the nth 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 ----> nth term
nth 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 nth term.
The formula to find the nth term is,
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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