Question: If the first two terms of an H.P. be $\frac{2}{5}$ and $\frac{12}{23}$ then the largest positive...

Question

If the first two terms of an H.P. be $\frac{2}{5}$ and $\frac{12}{23}$ then the largest positive term of the progression is the

Answer 1

For the corresponding A.P., the first two terms are $\frac{5}{2}$ and $\frac{23}{12}$ i.e. $\frac{30}{12}$ and $\frac{23}{12}$

Common difference $= - \frac{7}{12}$

∴ The A.P. will be $\frac{30}{12},\frac{23}{12},\frac{16}{12},\frac{9}{12},\frac{2}{12}, - \frac{5}{12},......$

The smallest positive term is $\frac{2}{12}$ , which is the 5^th term.

∴The largest positive term of the H.P. will be the 5^th term.

Question: If the first two terms of an H.P. be \(\frac{2}{5}\) and \(\frac{12}{23}\) then the largest positive...