Points to Remember: Arithmetic Progression Class 10 Notes | EduRev

Mathematics (Maths) Class 10

Class 10 : Points to Remember: Arithmetic Progression Class 10 Notes | EduRev

 Page 1


Arithmetic 
Progressions 
Page 2


Arithmetic 
Progressions 
a - rst number of an A. P . d - common dierence of an A. P . a
n
 - term of an A. P . n - number of terms
A sequence of numbers in which each diers from the preceding one by a constant quantity (common dierence).
If the sequence is increasing, common dierence is positive; if it is decreasing, common dierence is negative.
15, 10, 5, 0, -5
       This formula is used to calculate sum of rst n terms.
       It can also be used to nd a or d when rest of the
information is given
       The same formula is used to calculate number of terms
when sum (s
n
) and a & d are given
means it adds all the numbers starting from the ?rst to n
th
[average of rst (a) & last term (l)] x n n
s
n
 =
a
 
+ l
2
s
n
 =        2a + (n - 1) d
n
2
3
4
5
1
a
n
 = a + (n - 1) d
 This formula is used to calculate :
The value of any term in A. P . when a, n, d is given
      Similarly, it can also be used to calculate d or a when
other imformation like a
n 
, n is given
      One can also use this to calculate numbers of term of 
an A. P .
+ 1
n =
a
n
 - a
d
a
n 
- last term
 
Where a
 
- rst term
 
1
2
3
Some important points :
s
1
 = a
1
1
s
n 
-
  
s
n - 1
 = a
n
2 a
n
 - a
m 
= (n - m) d 3
a
n
 - a
n - 1 
= d
4
ARITHMETIC PROGRESSIONS 12
Arithmetic Progressions
Page 3


Arithmetic 
Progressions 
a - rst number of an A. P . d - common dierence of an A. P . a
n
 - term of an A. P . n - number of terms
A sequence of numbers in which each diers from the preceding one by a constant quantity (common dierence).
If the sequence is increasing, common dierence is positive; if it is decreasing, common dierence is negative.
15, 10, 5, 0, -5
       This formula is used to calculate sum of rst n terms.
       It can also be used to nd a or d when rest of the
information is given
       The same formula is used to calculate number of terms
when sum (s
n
) and a & d are given
means it adds all the numbers starting from the ?rst to n
th
[average of rst (a) & last term (l)] x n n
s
n
 =
a
 
+ l
2
s
n
 =        2a + (n - 1) d
n
2
3
4
5
1
a
n
 = a + (n - 1) d
 This formula is used to calculate :
The value of any term in A. P . when a, n, d is given
      Similarly, it can also be used to calculate d or a when
other imformation like a
n 
, n is given
      One can also use this to calculate numbers of term of 
an A. P .
+ 1
n =
a
n
 - a
d
a
n 
- last term
 
Where a
 
- rst term
 
1
2
3
Some important points :
s
1
 = a
1
1
s
n 
-
  
s
n - 1
 = a
n
2 a
n
 - a
m 
= (n - m) d 3
a
n
 - a
n - 1 
= d
4
ARITHMETIC PROGRESSIONS 12
Arithmetic Progressions
Tricks to remember
formulae and tips to 
solve 
dicult questions.
Introduction of
Arithmetic 
Progressions
Problem solving based
on a
n
.
How to avoid
mistakes in
Arithmetic 
Progressions
Scan the QR Codes to watch our free videos
 For determining the A.P . or to nd next terms of A.P . always try
to nd ‘a’ and ‘ d’ .
 There are two formulas in AP and each of them is assembled of
4 variables. We use these formulas to nd one missing variable when
the information about the other three are given.
PLEASE KEEP IN MIND
 
If it talks about, price/ rent/ fare on a particular time (day,
month, hour) then it’s a question of a
n 
.
 
When sum of two terms or addition two A.P . ’s is given, then 
write them in the from of ‘a+nd ’ and solve the two formed 
linear equations simultaneously.
?
?
?
 
When relation between any two terms of a sequence is given in 
whatever way try to write them in the form of  ‘a+nd’ and then solve 
for ‘n’ , ‘a’ or  ‘ d’ .
?
 
 
To know the number of terms(n), rst term (a), common 
dierence (d), we can use any of the two formulas (a
n
& S
n
). The only 
thing is to recogise whether information about the sum or term 
of A.P . is given.
?
 
There are questions where we have to nd multiple of a number,
divisible by a number, when divided by this number leaves remainder,
in all these types of questions the common dierence is that number 
only.
?
?
?
 To recognise whether the sequence of a number is forming an 
A.P .  or not, we should check for the common dierence that should be 
equal.
 In word problems, when it talks about total rent/ fare/ amount
 or something like that then it’s a question on S
n
.
 
?
ARITHMETIC PROGRESSIONS 13
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