Let the common difference be d.
The sum of the first four terms is
5 + (5+d) + (5+d+d) + (5+d+d+d)
= 20 + 6d
The sum of the next 4 terms is
5+4d + 5+5d + 5+6d + 5+7d = 20 + 22d
You have been told that
20 +6d = (1/2)(20 + 22d)= 10 + 11d
Therefore
5d = 10
d = 2
Check: does
5+7+9+11 = (1/2)(13+15+17+19) ?
32 = (1/2)(64)
find the common difference of A.P whose first term is 5 and the sum of its first 4 terms is half the sum of next 4 terms
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2. Find A.P Which fifth term is 5 and common difference is -3.
Given 5th term is 5 and common difference is -3
a5 = a +4d
5 = a -12
a = 17
So the AP is 17 , 14 , 11
a5 = a +4d
5 = a -12
a = 17
So the AP is 17 , 14 , 11
1 answer