an arithmetic progression has 3 as its first term. also the sum of the first 8 terms is twice the sum of the first 5 terms. find the common difference.
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let a be the first term and d be the common difference
given a=3
S8=2xS5 ....(i)
now Sn= (n/2 ) * (2a + (n-1) d)
using (i)
(8/2)(6+7d) = 2 (5/2)(6+4d)
which is a linear in d, solving this will give us our common difference d.
4*(6+7d)= 5*(6+2d)
24+28d=30+10d
18d=6
d= 6/18 = 1/3
I hope I didn't do any silly mistakes and this helps.
given a=3
S8=2xS5 ....(i)
now Sn= (n/2 ) * (2a + (n-1) d)
using (i)
(8/2)(6+7d) = 2 (5/2)(6+4d)
which is a linear in d, solving this will give us our common difference d.
4*(6+7d)= 5*(6+2d)
24+28d=30+10d
18d=6
d= 6/18 = 1/3
I hope I didn't do any silly mistakes and this helps.
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