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

## 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 dierence of an A. P . a
n
- term of an A. P . n - number of terms
A sequence of numbers in which each diers from the preceding one by a constant quantity (common dierence).
If the sequence is increasing, common dierence is positive; if it is decreasing, common dierence 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 dierence of an A. P . a
n
- term of an A. P . n - number of terms
A sequence of numbers in which each diers from the preceding one by a constant quantity (common dierence).
If the sequence is increasing, common dierence is positive; if it is decreasing, common dierence 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
dicult 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
dierence (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 dierence 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 dierence 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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## Mathematics (Maths) Class 10

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