Basic Of Arithmetic Progression(AP)
1,2,3,4,5,6,7,8. here 2-1=3-2=4-3......difference same every where so in AP. (Common Difference=> 2-1=1.)
her in all case difference is same and equal to 1. so Common Difference(cd)=1.
2,4,6,8,10,12,14. here 4-2=6-4=8-6......difference also same every where so in AP.
her in all case difference is same and equal to 2. si Common Difference(cd)=2.
etc.
Note: Common Difference(cd) may be Positive, Negative or Zero.
Let's say a is First Term d is Common Difference then AP(Arithmetic Progression) can be defined as...
a, a+d, a+2d, a+3d, a+4d,..........
Finite Arithmetic Progression(AP): In AP if the number of terms are finite then called Finite Arithmetic Progression(AP).
Examples:
1,2,3,4,5,6,7,8........20. here mentioned that you have to go up to 20 only, so finite Number.
2,4,6,8,10. here already mentioned finitely.
Term (General Term): Sometimes it is also called Last Term, since we can find Last Term by using General Term Formula().
=a+(n-1)d
here,
= | the nᵗʰ term in the sequence | |
a = First term of an AP,
n = No of terms in an AP,
d = Common Difference,
Let's take an Example: 2,4,6,8,10,12,....20.
a= 2,
n=10,
d=4-2=6-4=8-6.....=2,
=ℓ=20.
We can find anything term by using the formula, if Series is in AP.
=a+(n-1)d
Infinite Arithmetic Progression(AP): In AP if the number of terms are Infinite then called Infinite Arithmetic Progression(AP).
Examples:
1,2,3,4,5,6,7,8......... here not mentioned that you have to go up to what place, so Infinite Number.
2,4,6,8,10........ here also not mentioned last term.
Last Term in AP: As the name suggest Last Term, means the Last number in AP is called Last Term.
Example:
2,4,6,8,10,12,14.................30. Here Last Term is 30.
This is generally denoted by ℓ (
एल).How to Find Summation Of AP(s) Series?
Let's say a First Term d Common Difference and is nᵗʰ term then AP(Arithmetic Progression) can be defined as...
a, a+d, a+2d, a+3d, a+4d,...........
S= sum of AP.
S= n/2[2a + (n – 1)d]
l = Last term of an AP.
nice
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