The 7th term of an AP is 4 times of 2nd term and 12th term is 2 more than 3times of its fourth term find the progression
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The 7th term of an AP is 4 times of 2nd term and 12th term is 2 more than 3times of its fourth term find the progression
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pls answer correctly ASAP
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since the seventh term of the A.P is 4 times of second term.
so,
we say, a+6d=4{a+d}
a+6d=4a+4d
2d=3a..........................................{1}
now, the twelvth term is 2 more than 3 times its fourth term,so we say,
a+11d=3{a+3d}+2
a+11d=3a+9d+2
2d=2a+2
d=a+1........................................{2}
putting the value of d in {1} we get,
2{a+1}=3a
2a+2=3a
a=2
now , putting the value of a in {2} we get,
d=2+1=3
d=3
now the A.P is
a,a+d,a+2d,a+3d.....................
putting the obtained value of a and d, we get,
2,5,8,11..............................
this is required A.P