Question

The ninth term of an AP is equal to seven times the second term and twelfth term exceeds five times the third term by 3. Find the first term and the common difference.

Answer 1

9 term of ap =a + 8d
2 term of ap =a+ d
ATQ
a+8d=7*a+d
a+8d=7a+7d
6a-d=0.....1
ATQ
12 term of ap is 5 times the third term
a+11d=3+5*a+2d
a+11d=3+5a+10d
4a-d =-3.....2
subtracting 2 from 1
6a-d=0
4a-d=-3
gives
2a=3
a=3\2
putting a in 1,
6*3\2-d=0
d=9
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