Question

7th term of a H.P is 3by2 and its 10th term is 12by 17 ...find 8th term

Answer 1

We know that, if a, b , c in H. P then 1/a , 1/b , 1/c are in A. P

Now, Given

7th Term of H. P = 3/2
10th term of H. P = 12/17

So, 7th term of A. P = 2/3
10 th term = 17/12

a + 6d = 2/3 = 8/12
a + 9d = 17/12

Subtracting the above equations,

a + 9d = 17/12
a + 6d = 8/12
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3d = 9/12 .
3d = 9/36 = 1/4 .


Now, Eighth term of A. P = a + 7d = (a + 6d)+d = 8/12 + 1/4 = 8/12+3/12 = 11/12 .

Now, Eighth term of H. P = 1/ 8th term of A. P = 1/11/12 = 12/11 .

Hope helped!