In first chapter of this course we discussed Number Systems , BODMAS rules and Algebra forumlas which help solve Arithmetic problems faster. If you have not yet read first chapter then read the first chapter first. In this chapter we will discuss about Series and other formulas helpful for calculation.
Series are integral part of every exam. In almost all exams you will get question of Series. In IBPS exams it is common to have 3 to 5 questions on series. Most series asked in exams are either combination or Arithmetic series or Geometric series.
So you should understand concept of Arithmetic series and Geometric Series by heart. Along with series I have given some useful formulas which will help you solve these type of problems easily.
Some Useful formulas for Sum of numbers
Sum of first n numbers = n ( n + 1 ) /2
Sum of first n odd numbers = n * n
Sum of first n even numbers = n ( n + 1 )
Sum of squares of first n numbers = n ( n + 1 ) ( 2n + 1 ) /6
Sum of cubes of first n numbers = n * n ( n + 1 ) * ( n + 1 ) / 4
Some Useful formulas for squares and cube root
If there are n digits in a number the square will have either 2n or 2n – 1 numbers
Square of a number can not end with 2, 3, 7. So in problems if you have these numbers at end then you can ignore the option
If number have 9 in end then its square root will have 3 or 7 in end.
If number have 5 in end then its square root will have 5 in end.
If number have 4 in end then its square root will have 2 or 8 in end.
If number have 6 in end then its square root will have 4 or 6 in end.
nth term of Arithmetic progression is = a ( n – 1 ) / d
Sum of n terms in Arithmetic Progression = n ( first term + last term ) /2
Sum of n terms in Arithmetic Progression = n ( 2a + (n – 1) * d ) /2
In above formulas a is the first term , d is the difference between the terms and n is the number of terms. For example if first terms is a then second term is a + d and so on.The series will look like
a , a+d , a+2d, … means each term will be added by d to get the next term for example
5,10,15 etc where each term is added by 5 to get the next term.
nth term of Geometric progression is = a r to the power ( n -1 )
Sum of n terms in Geometric Progression = a ( 1 – r to the power n ) / ( 1 – r )
In both of above formulas a is the first term and r is the difference between the numbers. For example first term will be a and second term will be ar and so on. The series will look like
a , a*r , a*r*r, … means each term will be multiplied by r to get the next term for example
5,10,20 etc where each term is multiplied by 2 to get the next term.
You can think of harmonic progression as opposite of Arithmetic progression. For example below series is in harmonic progression
1/a , 1/(a+d) , …… 1/(a + nd)
where 1/a is the first term and d is the difference. n is the number of terms. For example
1/5,1/10,1/15 etc where each denominator is added by 5 to get the next term.
Important Series formulas
HCF and LCM of numbers
HCF of decimals
First make sure all numbers have same number of digits after decimal. You can add zeros at the end to make digits after decimal same in all numbers. Then find HCF of numbers removing the decimals. Once you have got the HCF make sure it also has same number of digits after decimal as the numbers had.
LCM of Decimals
Same as above but you need to find LCM of numbers.
HCF of fractions
HCF = HCF of numerators / LCM of denominators
LCM of fractions
LCM = LCM of numerators / HCF of denominators
Important Formula for exams
LCM * HCF = Product of two numbers. Say if numbers are a and b then
LCM of a and b multiplied by HCF of a and b is equal to a multiplied by b.
If HCF of two numbers a and b is H then (a+b) and (a-b) are divisible by H.
If a and b give remainder p and q when divided by H then H is HCF of (a-p) and (b-q)
We will now head over to the third chapter of this tutorial.