Question

If 9th term is 75 and 21st term is 183 of an A.P then find its t81​

Answer 1

Question:-

If 9th term is 75 and 21st term is 183 of an A.P then find its t81.

Answer:-

Given,

➦ 9th term is 75

➦ 21st term is 183

Now,

➣ tn = a + ( n - 1 ) d

➣ t 9 = a + ( 9 - 1 ) d

➣ 75 = a + 8d .......... ( 1 )

And,

➣ tn = a + ( n - 1 ) d

➣ t 21 = a + ( 21 - 1 ) d

➣ 183 = a + 20d .......... ( 2 )

Then,

Subtract ( 1 ) from ( 2 )

a + 20d = 183 .......... ( 2 )

-a ±8d = - 75 .......... ( 1 )

12d = 108

d = 108/12

$\boxed{ \: d \: = \: 9 \: }$

Substitute d in equation ( 1 ):-

➣ a + 8(9) = 75

➣ a + 72 = 75

➣ a = 75 - 72

➣ $\boxed{ \: a \: = \: 3 \: }$

Now,

➣ t 81 = 3 + ( 81 - 1 ) 9

➣ t 81 = 3 + 80(9)

➣ t 81 = 3 + 720

➣ t 81 = 723

∴ 81th term is 723.

Verification:-

➦ a + 20d = 183

➦ 3 + 20(9) = 183

➦ 3 + 180 = 183

➦ 183 = 183

Answer 2

$hey \: mate$

Question:-

If 9th term is 75 and 21st term is 183 of an A.P then find its t81.

Answer:-

Given,

➦ 9th term is 75

➦ 21st term is 183

Now,

➣ tn = a + ( n - 1 ) d

➣ t 9 = a + ( 9 - 1 ) d

➣ 75 = a + 8d .......... ( 1 )

And,

➣ tn = a + ( n - 1 ) d

➣ t 21 = a + ( 21 - 1 ) d

➣ 183 = a + 20d .......... ( 2 )

Then,

Subtract ( 1 ) from ( 2 )

a + 20d = 183 .......... ( 2 )

-a ±8d = - 75 .......... ( 1 )

12d = 108

d = 108/12

\boxed{ \: d \: = \: 9 \: }

d=9

Substitute d in equation ( 1 ):-

➣ a + 8(9) = 75

➣ a + 72 = 75

➣ a = 75 - 72

➣ \boxed{ \: a \: = \: 3 \: }

a=3

Now,

➣ t 81 = 3 + ( 81 - 1 ) 9

➣ t 81 = 3 + 80(9)

➣ t 81 = 3 + 720

➣ t 81 = 723

∴ 81th term is 723.

Verification:-

➦ a + 20d = 183

➦ 3 + 20(9) = 183

➦ 3 + 180 = 183

➦ 183 = 183