in third term of h.p is one by seven and 15 is one by 31 and their series is
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3rd term of a HP = 1/7
15th term of same HP = 1/31
we know,
nth term of an HP = 1/{a + (n -1)d}
1/7 = 1/{a + (3 -1)d }
1/7 = 1/(a +2d )
7 = a + 2d -------(1)
similarly,
1/31 = 1/(a +(15-1)d }
31 = a + 14d --------(2)
from equations (1) and (2)
24 = 12d
d = 2 put equation (1) ,a = 3
now, the series are,
1/3 , 1/5 , 1/7, 1/9 , 1/11.......
15th term of same HP = 1/31
we know,
nth term of an HP = 1/{a + (n -1)d}
1/7 = 1/{a + (3 -1)d }
1/7 = 1/(a +2d )
7 = a + 2d -------(1)
similarly,
1/31 = 1/(a +(15-1)d }
31 = a + 14d --------(2)
from equations (1) and (2)
24 = 12d
d = 2 put equation (1) ,a = 3
now, the series are,
1/3 , 1/5 , 1/7, 1/9 , 1/11.......
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