HOW TO FIND THE SUM OF ARITHMETIC SERIES

How to Find the Sum of Arithmetic Series ? 

To find the sum of an arithmetic series, we use the formula give below.

Sn  =  (n/2) [a + l] (or)

Sn  =  (n/2) [2a + (n - 1)d]

a = first term, d = common difference, n = number of terms and l = last term.

How to Find the Sum of Arithmetic Series - Examples

Question 1 :

Find the sum of the following APs

(i)  2 , 7 , 12,....... to 10 terms

Solution :

S n = (n/2) [2a + (n - 1) d]

n = 10   a = 2   d = 7 - 2  =  5

 S10  =  (10/2) [2(2) + (10-1)5]

  =  5 [4 + 9(5)]

  =  5 [4 + 45]

  =  5 [49]

  =  245

(ii) -37,-33,-29,..................... to 12 terms

Solution :

S n = (n/2) [2a + (n - 1) d]

n = 12   a = -37   d = -33 - (-37)

                            = -33 + 37

                            = 4

 S12  =  (12/2) [ 2 (-37) + (12 - 1) 4 ]

  =  6 [ -74 + 11 (4) ]

  =  6 [ -74 + 44 ]

  =  6 [-30]

  =  -180

(iii) 0.6, 1.7, 2.8,............... to 100 terms

Solution :

S n = (n/2) [2a + (n - 1) d]

n = 100   a = 0.6   d = 1.7 - 0.6

                            = 1.1

S100  =  (100/2) [ 2 (0.6) + (100 - 1) 1.1 ]

  =  50 [ 1.2 + 99 (1.1) ]

  =  50 [1.2 + 108.9 ]

  =  50 [110.1]

  =  5505

(iv) 1/15, 1/12, 1/10,................... to 11 terms

Solution :

S n = (n/2) [2a + (n - 1) d]

n = 11    a = 1/15   d = (1/12) - (1/15)

                            = (5 - 4)/60

                           = 1/60

S11  =  (11/2) [ 2 (1/15) + (11 - 1) (1/60) ]

  =  (11/2) [(2/15) + (10/60)]

  =  (11/2) [(2/15) + (1/6)]

  =  (11/2) [ (4 + 5)/30 ]

  =  (11/2) [ 9/30 ]

  =  (11/2) [ 3/10 ]

  =  33/20 

Question 2 :

Find the sums given below

(i) 7 + 10   1/2 + 14 + ...............+ 84

Solution :

S n = (n/2) [a + l]

 a = 7   d = (21/2) - (7)         l = 84

              = (21 - 14)/2

              = 7/2

an  =  a + (n - 1) d

84  =  7 + (n - 1) (7/2)

84 - 7  =  (n - 1) (7/2)

77 x (2/7)  =  n - 1

11 x 2  =  n - 1

  n - 1  =  22

    n  =  22 + 1  =  23

So, the total number of terms in the given series is 23.

S23 = (23/2) [7 + 84]

 S23 = (23/2) [91]

        = 2093/2 

After having gone through the stuff given above, we hope that the students would have understood, how to find the sum of arithmetic series.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. Angular Speed and Linear Speed

    Dec 07, 22 05:15 AM

    Angular Speed and Linear Speed - Concepts - Formulas - Examples

    Read More

  2. Linear Speed Formula

    Dec 07, 22 05:13 AM

    Linear Speed Formula and Examples

    Read More

  3. Angular Speed and Linear Speed Worksheet

    Dec 07, 22 05:08 AM

    Angular Speed and Linear Speed Worksheet

    Read More