Question

the sum of the first 4 terms of an arithmetic sequence is 72.sum of the first 9 terms is also 72 . what is the fifth term of the sequence

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Answer 1

Answer:

fifth term a5 = 8

Step-by-step explanation:

given S4 = 72 and S9 = 72

to find a5

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

therefore S4 = 4/2 [ 2a + 3d ] [ n = 4 ]

=> S4 = 4a + 6d

=> 72 = 4a + 6d

=> 36 = 2a + 3d-----------------1. [ dividing throughout by 2]

similarly, S9 = 9/2 [ 2a + 8d ]

=> 72 = 9a + 36d

=> 8 = a + 4d------------2 [ dividing throughout by 9 ]

2a + 3d = 36 ------------1

a + 4d = 8---------------2

multiply equation 2 by -2, we get

2a + 3d = 36

-2a - 8d = -16

adding both, we get

-5d = 20

=> d = -4

substituting value of d in equation 1, we get

2a + 3(-4) = 36

=> 2a - 12 = 36

=> 2a = 48

=> a = 24

now fifth term => a5 = a + 4d

=> 24 + 4(-4)

=> 24 - 16

=> 8