# EXAMPLES OF FINDING THE SUM OF AN ARITHMETIC SERIES

Examples of Finding the Sum of an Arithmetic Series :

Here we see some example problems to show the sum of finding 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.

## Examples of Finding the Sum of an Arithmetic Series

Question 1 :

Find the sum of the series

34 + 32 + 30 + .................. + 10

Solution :

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

a = 34, d = 32 - 34  =  -2, l = 10 = a n

an  =  a + (n - 1) d

10  =  34 + (n - 1) (-2)

10 - 34  =  (n - 1) (-2)

-24  =  (n - 1) (-2)

-24/(-2)  =  (n - 1)

12  =  n - 1

n  =  12 + 1

n  =  13

Hence the number of terms in the sequence is 13.

S13  =  (13/2) [34 + 10]

S13  =  (13/2) [ 44]

=  13(22)

=  286

Question 2 :

Find the sum of the series

- 5 + (-8) + (-11) + .............+ (-230)

Solution :

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

a = -5    d = -8 - (-5)         l = -230 = an

= -8 + 5

= -3

an  =  a + (n - 1) d

-230  =  -5 + (n - 1) (-3)

-230 + 5  =  (n - 1) (-3)

-225  =  (n - 1) (-3)

225/3  =  (n - 1)

75  =  n - 1

n  =  75 + 1

n  =  76

Hence the number of terms in the sequence is 76.

S76 = (76/2) [-8 + (-5)]

S76 = 38 [ -8 - 5]

=  38 (-13)

=  -494

Question 3 :

In an AP

Given a = 5, d = 3, a n= 50 find n and Sn

Solution :

an = a + (n - 1) d

50 = 5 + (n - 1) (3)

50 - 5 = (n - 1) (3)

45 = (n - 1) (3)

45/3 = n - 1

n - 1 = 15

n = 15 + 1

n = 16

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

S16 = (16/2) [5 + 50]

=  8 (55)

=  440

After having gone through the stuff given above, we hope that the students would have understood, examples of finding the sum of an 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

## Recent Articles

1. ### SAT Math Videos

May 22, 24 06:32 AM

SAT Math Videos (Part 1 - No Calculator)

2. ### Simplifying Algebraic Expressions with Fractional Coefficients

May 17, 24 08:12 AM

Simplifying Algebraic Expressions with Fractional Coefficients