d) The sum of the ten terms of an A.P. is 50 and its fifth term is treble the
second term. Calculate the first term and the sum of first twenty terms.
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S10=50
T5 = 3×T2
a+4d = 3 ( a+d)=3a +3d
a+4d = 3a +3d
--2a +1d =0
--2a = -1d
2a =d
d=2a
Sn = n/2 ( 2a +( n -1)d)
S10 = 10/2 ( 2a+9 ×2a )
= 5×20a
100a =50
a =1/2
d = 2×1/2 =1
S20= 20/2 ( 1+ 19 ×1)
= 10× 20 =200
The required 1st term 1/2
common difference d =1
sum of 20 terms is 200
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