For an arithmetic progression with an initial term 'a' and a common difference 'd' between successive members, the nth term of the sequence is expressed as
a_{n} = a+(n−1)d, where ,…n = 1,2,… and so forth.
An Arithmetic Progression, also known as an Arithmetic Sequence, is a sequence of numbers or terms where the difference between consecutive terms remains constant. Below are some straightforward tips and tricks to help you swiftly, easily, and efficiently solve Arithmetic Progression questions in competitive exams.
An Arithmetic Progression is Represented in the form a, (a + d), (a + 2d), (a + 3d), …
where a = the first term, and d = the common difference.
n is number of Terms
General form, T_{n} = a + (n1)d
Where T_{n }is nth term of an Arithmetic Progression
t_{n} = a + (n – 1)d
where t_{n} = nth term,
a= the first term ,
d= common difference,
n = number of terms in the sequence
In the given series,
a (first term) = 1
d (common difference) = 2 (3 – 1, 5 – 3)
Therefore, 10^{th} term = t_{10} = a + (n1) d
t_{10} = 1 + (10 – 1) 2
t_{10} = 1 + 18
t_{10} = 19
Example 2: Find last term in the series if there are 8 term in this series 13 , 17 , 21 ,25….
(a) 33
(b) 41
(c) 37
(d) 39
Ans: (b)
We know that,
t_{n} = a + (n – 1)d
where t_{n} = nth term,
a = the first term ,
d = common difference,
n = number of terms in the sequence
In the given series,
a (first term) = 13
d (common difference) = 4(17 – 13, 21 – 17)
Therefore, 8^{th} term = t_{8 }= a + (n1) d
t_{8} = 13 + (8 – 1) 4
t_{8} = 13 + 28
t_{8} = 41
Example 1: Find the number of terms in the series 7, 11, 15, . . .71
(a) 12
(b) 25
(c) 22
(d) 17
Ans: (d)
We know that,
where n = number of terms,
a= the first term,
l = last term,
d= common difference
In the given series,
a (first term) = 7
l (last term) = 71
d (common difference) = 11 – 7 = 4
n = 16 + 1
n = 17
Example 2: Find the number of terms if First term = 22 ,Last term = 50 and common difference is 4
(a) 10
(b) 9
(c) 8
(d) 7
Ans: (c)
We know that,
where n = number of terms,
a = the first term,
l = last term,
d = common difference
In the given series,
a (first term) = 22
l (last term) = 50
d (common difference) = 4
n = 7+ 1
n = 8
Example 1: Find the sum of the series 1, 3, 5, 7…. 201
(a) 12101
(b) 25201
(c) 22101
(d) 10201
Ans: (d)
We know that,
OR
where,
a = the first term,
d= common difference,
l = tn = nth term = a + (n1)d
In the given series,
a = 1, d = 2, and l = 201
Since we know that, l = a + (n – 1) d
201 = 1 + (n – 1) 2
201 = 1 + 2n 2
202 = 2n
n = 101
S_{n} = 50.5 (1 + 201)
S_{n} = 50.5 x 202
S_{n} = 10201
Example 2: Find the sum of the Arithmetic series if First term of this series is 45 , common difference is 5 and number of terms in this series is 8.
(a) 500
(b) 300
(c) 400
(d) 200
Ans: (a)
We know that,
OR
where, a = the first term,
d = common difference,
l = tn = nth term = a + (n1)d
In the given series,
a = 45, d = 5, and n = 8
S_{n} = 4 (90 + 35)
S_{n} = 4 x 125
S_{n} = 500
Example 1: Find the arithmetic mean of first five prime numbers.
(a) 6.6
(b) 3.6
(c) 5.6
(d) 7.6
Ans: (c)
We know that
Here, five prime numbers are 2, 3, 5, 7 and 11
Therefore, their arithmetic mean (AM)
Example 2: Find Second Number if arithmetic mean of two numbers is 24 and First number is 10.
(a) 32
(b) 38
(c) 34
(d) 36
Ans: (b)
We know that
Let second Number is b
Therefore, their arithmetic mean (AM)
b = 38
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1. What is an arithmetic progression? 
2. How can I find the nth term of an arithmetic progression? 
3. What is the formula to find the sum of an arithmetic progression? 
4. How can I determine if a given sequence is an arithmetic progression? 
5. Are there any tricks to quickly identify the common difference in an arithmetic progression? 
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