The 18th term of an A.P is half of its second term and 11th term exceeds one third of its 4th term by 1.find the 15th term.
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let the first term be a and the common difference be d
a+17d=1/2(a+d)
2a+34d=a+d
a+33d=0 -------- equation 1
a+10d- {1/3(a+3d)=1
a+10d-(a+3d)/3=1
3a+30d-a-3d=3
2a+27d=3 -------- equation 2
2a+66d=0
2a+27d=3
=39d=-3
=d=-1/13
and a=33/13
the 15th term=a+14d
33/13+14×-1/13
33-14/13
19/13
a+17d=1/2(a+d)
2a+34d=a+d
a+33d=0 -------- equation 1
a+10d- {1/3(a+3d)=1
a+10d-(a+3d)/3=1
3a+30d-a-3d=3
2a+27d=3 -------- equation 2
2a+66d=0
2a+27d=3
=39d=-3
=d=-1/13
and a=33/13
the 15th term=a+14d
33/13+14×-1/13
33-14/13
19/13
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