The sum of sixth term of AP is 42the ratio of 10th term of the 30th term is 1:3 find the first term of AP
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a+41d=42.......(1)
a+9d/a+29d=1/3
3(a+9d)=a+29d
3a+27d=a+29d
3a-a+27d-29d=0
2a-2d=0
2(a-d)=0
a-d=0
a=d.......put in (1)
a+41d=42
a+41a=42
42a=42
a=1
a+9d/a+29d=1/3
3(a+9d)=a+29d
3a+27d=a+29d
3a-a+27d-29d=0
2a-2d=0
2(a-d)=0
a-d=0
a=d.......put in (1)
a+41d=42
a+41a=42
42a=42
a=1
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