What is Arithmetic Progression?
In mathematics an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers in which the difference between any two consecutive numbers or expressions is the same.
Tn = a + (n-1)d -------------------- To find n term |
| Formula for arithmetic progression |
Sn = n [2a + (n-1)d] --------------------- To find sum
2
Sn = n [a + l] --------------------- Last Term
2
Note:
a = First term.
I = Last term.
Here, have 4 numbers which is
3,6,9,12.
To know either this number is arithmetic or geometric is find the common difference between the two number.And at A.P is only can "-" or "+".
For example:
3,6,9,12
Find the common difference first!
- 6-3 = 3
- 9-6 = 3
- 12-9 = 3
So, if the number is same,that mean its belong to arithmetic progression.
another method,easy ways how to calculate arithmetic progression is identified each number first!
a - i called it as first term which is equal to n.
d - different between each number.
l - last term.
So,the first term is 3, the different between two number is 3 and 12 is as last term.
Example 1
Given the following number :-
2,4,6,8,10,..........
a) Find the 105th term of the sequence.
b) Calculate the sum of the series until the 63rd term.
c) Calculate the sum of the series given until the final term is 1064.
The Question ask to find the 105th term of the sequence.
Step 1 :
Find the difference between the number first!
4-2 = 2
6-4 = 2
8-6 = 2
10-8 = 2
d=4-2 = 2
a=2 (the first term)
n=105
Formula:
Tn = a + (n-1)d
Step 2 :
Include all the information above into the formula
d=4-2 = 2
a=2 (the first term)
n=105
T10 = 2 + (105-1)x 2
Step 3 :
Minuse "d" and "1" first.
Then,multiply "d" with "n" and 1
T10 = 2 + (105-1)x 2
= 2 + (104) x 2
Step 4 :
Plus the first term (2) after (2) multiply with (104)
T10 = 2 + 208
= 210
The 105th term of the sequences is 201.
Overview working:
Tn10 = 2 + (105-1)2
= 2 + (104)2
= 2 + 208
=210
Okey, that all for today :)
Best way to learn ever! Thanks.
BalasPadam