Question

If 3rd and 8th terms of HP are 1/4 and 2/3 then 9th term is

Answer 1

Answer:

$3rd \: term \: = \frac{1}{4} \\ 8 {}^{th} term = \frac{2}{3} \: \: \: of \: hp \\ \\ \frac{1}{a + 2d} = \frac{1}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {1}^{st \: } equation \\ \\ \\ \frac{1}{a + 7d} = \frac{2}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: {2}^{nd} equation \\ \\ \\ using \: cross \: multiplication \: on \: both \: equation \\ \\ \\ a + 2d = 4 \\ 2a + 14d = 3 \\ \\ \\ find \: a \: and \: d \: using \: elimination \: method \\ \\ we \: find \: \: \: \: \: a = 5 \: and \: d = \frac{ - 1}{2} \\ \\ {9}^{th} \: term \: of \: hp \: is \: \frac{1}{a + 8d} \\ \\ \frac{1}{5 + 8 \times \frac{ - 1}{2} } \\ \frac{1}{5 + ( - 4)} \\ = 1 \\ {9}^{th \: } of \: hp \: is \: 1$

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