Question

If 9th term of Ap is 8 and 7th term of Ap is 6 then
find 4th term?​

Answer 1

$\large \bf \clubs \:  Given :-$

For an A.P.

• 7th Term = 6

• 9th Term = 8

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$\large \bf \clubs \:  To \: Find :-$

• 4th Term of the  A.P.

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$\large \bf \clubs \:  Formula \: For \: nth \: Term :-$

$\large \bf{a_n= a + (n - 1)d}$

Where :

• a = First term

• d = Common difference

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$\large \bf \clubs \:  Solution :-$

We Have ,

$\large \sf{a_{7} = 6}\\ \\ \large \sf a + 6d = 6\: \: - - - (1)\\ \\ \large \sf{a_{9} = 8} \\ \\ \large:\longmapsto \sf a + 8d = 8 \: \: - - - (2)$

Subtracting (1) From (2) , We get :-

$\sf2d = 2 \\ \\ \sf d = \cancel{\frac{2}{2} }\\ \\ \purple{ \Large :\longmapsto  \underline {\boxed{{\bf d = 1} }}}$

Putting Value of d in (1) :

$:\longmapsto \sf a + 6 \times 1 = 6 \\ \\ :\longmapsto \sf a + 6 = 6 \\ \\ \purple{ \Large :\longmapsto  \underline {\boxed{{\bf a = 0} }}}$

Now ,

$\large\sf4th \: term = a_4 \\ \\ \large= \sf a + 3d \\ \\ \large= \sf0 + 3 \times 1 \\ \\ \Large= \pmb{\frak \green{3}}$

So ,

$\Large \underline{ \pmb{ \pink{ \maltese \: \: \underline\frak{4th \: \text{T}erm = 3}}}}$

$\Large\red{\mathfrak{  \text{W}hich \:\:is\:\: the\:\: required} }\\ \LARGE \red{\mathfrak{ \text{ A}nswer.}}$

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Answer 2

Answer:

♧♧Given:-

In the given AP ,

• 7th term of an Ap=6

• 9th term of an Ap= 8

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♧♧To prove:-

• Fourth term of an Ap.

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♧♧Proof:-

♧♧We know the formula of nth term of an Ap

an= a+(n-1)d

♧♧Here,

• a=first term of an Ap

• d=common difference.

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♧♧Lets enter to your question,

Here we have that,

a7 = 6

a+6d = 6 (i)

a9 = 8

a+8d = 8 (ii)

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♧♧Now by subtracting both of the equations (i) and (ii)

♤♤We will get that,

a +8d = 8

a +6d = 6

0+2d = 2

2d = 2

d = 2/2

♤d = 1

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♧♧Putting the value of f in 2 equation: -

a + 8d = 8

a + 8 (1) = 8

a + 8 = 8

a = 8-8

♤a = 0

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♧♧Let 4th term of an Ap,

= a + 3d

♧♧Now applying the values of a and d .

♧♧we get,

= a + 3d

= 0 + 3 (1)

= 0 + 3

= 3

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♧♧Verification: -

Hence the required answer,

♧ 4th term of an Ap is 3.

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♧♧Hope it helps u mate

♧Answered by Rohith kumar maths dude