If an A-P- is such that a 4-a7-2-3- find a 6-a8

A_4/a_7 = 2/3 [Given] ⇒a+3d/a+6d = 2/3⇒ 3a + 9d = 2a +12d ⇒ a = 3d ...... (i) a_6/a_8 = a+5d/a+7d ⇒3d+5d/3d+7d [∵ 3d from (i)] ⇒8d/10d⇒4/5 ∴a_6/a_8 ...

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Standard XII

Mathematics

nth Term of A.P

If an A.P. is...

Question

If an A.P. is such that $\frac{a_{4}}{a_{7}} = \frac{2}{3}$ , find $\frac{a_{6}}{a_{8}}$

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Solution

$\frac{a_{4}}{a_{7}} = \frac{2}{3}$ [Given]
$\Rightarrow \frac{a + 3 d}{a + 6 d} = \frac{2}{3} \Rightarrow 3 a + 9 d = 2 a + 12 d$
$\Rightarrow a = 3 d$ ...... (i)
$\frac{a_{6}}{a_{8}} = \frac{a + 5 d}{a + 7 d}$
$\Rightarrow \frac{3 d + 5 d}{3 d + 7 d}$ $[∵ 3 d f r o m (i)]$
$\Rightarrow \frac{8 d}{10 d} \Rightarrow \frac{4}{5}$
$∴ \frac{a_{6}}{a_{8}} = \frac{4}{5}$

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Similar questions

Q. For

A P

a_{1}, a_{2}, a_{3},

..., if

\frac{a_{4}}{a_{7}} = \frac{2}{3}

, find

\frac{a_{6}}{a_{8}}

Q. Let

a_{1}, a_{2}, a_{3}, \dots

be an A.P. such that

a_{3} + a_{5} + a_{8} = 11

and

a_{4} + a_{2} = - 2

. Then the value of

a_{1} + a_{6} + a_{7}

Q. If

a_{n}

is the

n^{th}

of an A.P. such that

a_{2} + a_{7} - a_{4} = 11

and

a_{3} + a_{8} = 24,

then

Q. For an A.P.,

a_{1}, a_{2}, a_{3}, \dots \dots

, if

a_{3} + a_{5} + a_{8} = 11

and

a_{4} + a_{2} = - 2

, then the value of

a_{1} + a_{6} + a_{7}

Q. Suppose

a_{2}, a_{3}, a_{4}, a_{5}, a_{6}, a_{7}

are integers such that

\frac{5}{7} = \frac{a_{2}}{2!} + \frac{a_{3}}{3!} + \frac{a_{4}}{4} + \frac{a_{5}}{5!} + \frac{a_{6}}{6!} + \frac{a_{7}}{7!}

where

0 \leq a < j

for

j = 2, 4, 5, 6, 7.

The sum

a_{2} + a_{3} + a_{4} + a_{5} + a_{6} + a_{7}

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If an A.P. is such that a4a7=23, find a6a8

a4a7=23 [Given] ⇒a+3da+6d=23⇒3a+9d=2a+12d ⇒a=3d ...... (i) a6a8=a+5da+7d ⇒3d+5d3d+7d [∵3d from (i)] ⇒8d10d⇒45 ∴a6a8=45

If an A.P. is such that $\frac{a_{4}}{a_{7}} = \frac{2}{3}$ , find $\frac{a_{6}}{a_{8}}$