Question

the 4th term of an ap is equal to three times the first term and the 7th term exceeds twise the third by 1 find the 1st term and common diffrence

Answer 1

Hey Friends,
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Let the first term be a and common difference be d
Then
t1=a
t4=a+3d
t7=a+6d
According to questn,
a+3d=3a
=> 2a-3d=0 ------(i)
Again,
a+6d=2(a+2d)+1
=> a+6d=2a+4d+1
=> a-2d=-1 -----(ii)

By multiplying 2 in eqn(ii)
2a-4d=-2 ------(iii)

By subtracting eqn(iii) from eqn(i)
2a-3d-2a+4d=2
d=2

Put the value of d in eqn(ii)
a-4=-1
a=3

Hope it's help you!!!!
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