Sequence and series
# Formulas
1. Sum of 1st n natural numbers Sn = 1+2+3+……. to n terms =
nn  1
2
2. Sum of 1st n even numbers Sn = 1 + 2 + 4 + to n terms = nn  1 .
3. Sum of 1st n odd numbers Sn = 1 + 3 + 5 +…… to n terms = n2
4. Sum of square 1st n natural numbers Sn= 12 + 22 + 32 +…………to n terms =
nn  12n  1
6
5. Sum of cubes of 1st n natural numbers Sn = 13 + 23 + 33 +………to n terms= [
nn  1 2
]
2
nn  1
6.  n =
2
nn  12n  1
7.  n 2 =
6

]2
n
n

1
8.  n 3 = [
2
# Rules to find General term
To find general terms we use following rules:
1) If the series/sequence is AS then tn= a + (n-1) d
2) If the series/sequence is GS then tn = arn-1
3) If the series/sequence is not both AS and GS we find a pattern.
4) If we cannot use all these methods mentioned above then tn = an2 + bn2 + c.
# Illustrative Examples
1. Find the sum of first 5 natural numbers.
Solution:
Here n =5
So, sn 
n(n  1) 5(5  1)

 15
2
2
2. Find the sum of first 10 even numbers.
Solution:
Here n = 10
So, sn  n(n  1)  10(10  1)  110
3. What is the sum of first 7 odd numbers?
Solution:
Here n = 7
So, sn  n 2  7 2  49
4. Calculate the sum of square of first three natural numbers?
Solution:
Here n = 3
sn 
n(n  1)(2n  1) 3(3  1)(6  1)

 14
6
6
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Sequence and series
5. Find the sum of cubes of first 5 natural numbers.
Solution:
Here, n = 5
n(n  1) 
 5(5  1) 
2
So, 
 = 15 = 225
 = 
 2 
 2 
2
2
# Important Questions for SLC Examination
1. Find the sum of the following series
a.1 + 3 + 5 + ………….. 25 terms
b.2 + 4 + 6 + ……….. 21 terms
c. 1 + 2 + 3 + …………. 25 terms
d. 2 + 4 + 6 + ……… 30 terms
e. 1 + 3 + 5 + ………… 50 terms
2. Find the sum of the following series
a.13 + 23 + 33 …………… +103
b.13 + 23 + 33 + …………… 8 terms
c. 12 + 22 + 32 + …………….. + 102
d.12 + 22 + 32 + ……….. 12 terms
3. Find the nth term and sum of n terms of following series.
a.22 + 42 + 62 + ……………… n terms
b. (1×2) + (2×3) + (3×4) + ……….. n terms
c. (2×4) + (3×5) + (4×6) + ………….. n terms
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