Write any three arithmetic progressions with sum of first five terms is 30.
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Answer:
a=2,d=2
a=4,d=1
a=0,d=3 are the APs
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The three arithmetic progressions with sum of first five terms is 30 are as follows.
Given,
Sn = 30
n = 5
we use the formula,
Sn = n/2 [ 2a + (n - 1) d ]
30 = 5/2 [ 2a + (5 - 1) d ]
12 = 2a + 4d
6 = a + 2d
(i)
when a = 2, d = (6 - a)/2 = (6 - 2)/2 = 2
the series is given by, 2, 4, 6, 8, 10
(ii)
when a = 4, d = (6 - a)/2 = (6 - 4)/2 = 1
the series is given by, 4, 5, 6, 7, 8
(iii)
when a = 8, d = (6 - a)/2 = (6 - 8)/2 = -2
the series is given by, 8, 6, 4, 2, 1
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