Questions For Practise

# Formulas
1.     Sum of 1st n natural numbers Sn = 1+2+3+……. to n terms =   
2.     Sum of 1st n even numbers Sn = 1 + 2 + 4 + to n terms = .
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 =
5.     Sum of cubes of 1st n natural numbers Sn = 13 + 23 + 33 +………to n terms= [ ] 2
6.       =
7.      2 =
8.      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
Find the sum of first 5 natural numbers.
Solution:
Here n =5
So, 
Find the sum of first 10 even numbers.
Solution:
Here n = 10
So,
What is the sum of first 7 odd numbers?
Solution:
Here n = 7
So,
Calculate the sum of square of first three natural numbers?
Solution:
Here n = 3

Find the sum of cubes of first 5 natural numbers.
Solution:
Here, n = 5
So,  =  = 152 = 225

# Important Questions for SLC Examination
Find the sum of the following series
1 + 3 + 5 + ………….. 25 terms
2 + 4 + 6 + ……….. 21 terms
1 + 2 + 3 + …………. 25 terms
 2 + 4 + 6 + ……… 30 terms
1 + 3 + 5 + ………… 50 terms
Find the sum of the following series
13 + 23 + 33 …………… +103
13 + 23 + 33 + …………… 8 terms
12 + 22 + 32 + …………….. + 102
12 + 22 + 32 + ……….. 12 terms
Find the nth term and sum of n terms of following series.
22 + 42 + 62 + ……………… n terms
 (1×2) + (2×3) + (3×4) + ……….. n terms
 (2×4) + (3×5) + (4×6) + ………….. n terms