Question

For AP a1,a2,a3.............if a4÷a7=2÷3, find a6÷a8

Answer 1

Your answer is in the following attachment.

Answer 2

Question: For an AP a₁, a₂, a₃........ If a₄/a₇ = 2/3, Find a₆/a₈

Given that,

$\hookrightarrow \ \sf \dfrac{a_4}{a_7} = \dfrac{2}{3}$

$\hookrightarrow \ \sf \dfrac{a + 3d}{a + 6d} = \dfrac{2}{3}$

We know than, $\sf a_n$ can be expressed as first term plus the product of of the position of the preceeding term and the common difference 'd'.

$\hookrightarrow \ \sf 3(a + 3d) = 2(a + 6d)$

$\hookrightarrow \ \sf 3a + 9d = 2a + 12d$

$\hookrightarrow \ \sf 3a - 2a = 12d - 9d$

$\large\boxed{\hookrightarrow \ \sf a = 3d}$

To Find,

$\hookrightarrow \ \sf \dfrac{a_6}{a_8}$

$\hookrightarrow \ \sf \dfrac{a + 5d}{a + 7d}$

Substituting the value of a = 3d above we get,

$\hookrightarrow \ \sf \dfrac{3d + 5d}{3d + 7d}$

$\hookrightarrow \ \sf \dfrac{8d}{10d}$

$\hookrightarrow \ \sf \dfrac{4d}{5d}$

$\hookrightarrow \ \sf \dfrac{4}{5}$

$\large\boxed{\therefore\sf \dfrac{a_6}{a_8} = \dfrac{4}{5}}$