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Question

Solve these three equations to get the value of a , n , d .
(2n1)d=10.5....(i)
n(a+(n1)d)=2d......(ii)
n(a+nd)=30.......(iii)

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Solution

Given,
(2n1)=10.5.........(i)
n(a+(n1)d)=2d.........(ii)
n(a+nd)=30............(iii)

eq(iii)eq(ii) gives
nd=302d
nd+2d=30........(iv)

2×eq(1), gives 4nd2d=21.........(v)

eq(iv)+(v), gives 5nd=51

2×eq(iv)....eq(i), gives 5d=49.5d=9.9

5nd=51

n=515d=515×9.9=5149.5=1.03

n=1.03

putting the values of n&d in eq (iii), we get

a=30nnd

=301.03515

=29.1210.2=18.92

a=18.92,n=1.03,d=9.9

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