EXAMPLES OF FINDING THE SUM OF AN ARITHMETIC SERIES

Question 1 :

Find the sum of the series

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

Solution :

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

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

a_n  =  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 = a_n

                 = -8 + 5

                 = -3 

a_n  =  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 :

a_n = 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

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