Question

the ninth term of an ap is equal to seven times the second term and the twelfth term exceeds five times the third term by 2 find the 1st term and the common difference

Answer 1

According to question
T9 = 7*T2
a+ 8d = 7(a+d)
a+ 8d = 7 a + 7d
-6a+ d = 0
d= 6a -------------(1)

Now,
T12= 5* T3 + 2
a+ 11d = 5(a+2d) + 2
a+ 11d = 5a+10d +2
-4a + d = 2
-4a + 6a = 2 (from equation 1)
2a = 2
a= 1

d= 6

First term = 1
Common difference = 6


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