# 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.

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