Math, asked by rajaradnam484, 1 year ago

find out 50th term
4th term 12
10th term 30

Answers

Answered by MisterIncredible
10

Question :-

Find out the 50th term of an AP . Whose 4th term is 12 and 10th term is 30 .

Answer :-

Given :-

4th term = 12

10th term = 30

Required to find :-

  • 50 term of the AP ?

Formula used :-

\dagger\large{\boxed{\rm{ {a}_{nth} = a + ( n - 1 ) d }}}

Solution :-

Given data :-

4th term = 12

10th term = 30

we need to find the 50th term of the AP .

So,

Let's consider the given information ;

4th term = 12

10th term = 30

However,

The 4th term can also be represented as " a + 3d "

=> a + 3d = 12 \longrightarrow{\tt{Equation - 1 }}

Consider this as equation - 1

Similarly,

The 10th term can be represented as " a + 9d "

=> a + 9d = 30 \longrightarrow{\tt{ Equation - 2 }}

consider this as equation - 2

Now,

Let's solve these 2 equations simultaneously using the elimination method .

 \tt{a + 9d = 30} \\  \tt{a + 3d = 12}  \\ \underline{( - )( - ) \: ( - ) \: } \\   \underline{\tt{ \:  \:  \:  \:  \:  \: \: 6d = 18}} \\  \\  \implies \tt{6d = 18} \\  \implies  \tt{d =  \frac{18}{6} } \\  \implies \tt{d = 3}

Hence,

  • Common difference ( d ) = 3

Substitute the value of d in equation 1

a + 3d = 12

a + 3 ( 3 ) = 12

a + 6 = 12

a = 12 - 6

a = 6

Hence,

  • First term ( a ) = 6

Using the formula ;

\dagger\large{\boxed{\rm{ {a}_{nth} = a + ( n - 1 ) d }}}

Let's find the 50th term ;

This implies ;

\rm{ {a}_{nth} = {a}_{50} }

\rm{ {a}_{50} = 6 + ( 50 - 1 ) 3 }

\rm{ {a}_{50} = 6 + ( 49 ) 3 }

\rm{ {a}_{50} = 6 +  147 }

\rm{ {a}_{50} = 153 }

Therefore ,

50th term = 153

Answered by Ataraxia
5

\LARGE\textbf{\mathrm{ANSWER}}

\Large\mathrm{ 4^{th} term  = 12}

\rm 10^{th} term = 30

\sf Common \:difference = {\frac{Term \: difference}{Position \: difference}

\sf Common \:difference = \frac{30-12}{10-4}

                          \sf = \frac{18}{6}

                          \sf={  3}

\sf First \: term = 4^{th} \: term -3d

             \sf = 12-3\times3

             \sf =12-9

             \sf = 3

\sf 50^{th} \: term = 1^{st} term +49d

             \sf = 3 + 49\times 3

             \sf = 3+147

             \sf =150

HOPE IT HELPS U ......

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