Question

the 3rd term of an Ap is 43 ,the 6th term is 76 what is the 20th term?(arethimetic sequense , class ten of keralla syllebus)

Answer 1

Hiii friend,

3Rd term = 43

A + 2D = 43---------(1)

And,


6th term = 76

A + 5D = 76----------(2)


From equation 1 we get,

A + 2D = 43

A = 43-2D------------(3)


Putting the value of A in equation (2)

A + 5D = 76

43-2D + 5D = 76

3D + 43 = 76

3D = 76-43

3D = 33

D = 33/3 => 11


Putting the value of D in equation (3)

A = 43-2D => 43 - 2 × 11 => 43 - 22 = 21


Therefore,


First term (A) = 21


And,
Common difference (D) = 11


20th term of an AP = A+19D

=> 21 + 19 × 11

=> 21 + 209

=> 230



Hence,

20th term of an AP = 230



HOPE IT WILL HELP YOU........ :-)

Answer 2

3rd term = a + 2d

43 = a + 2d

a = 43 - 2d ---1equation

------------------

6th term = a + 5d

76 = a + 5d

Putting the value of a from 1equation,

76 = 43 - 2d + 5d

76 - 43 = 3d

33 = 3d

33/3 = d

11 = d
------------------
Putting the value of d in 1equation,

a = 43 - 2d
a = 43 - 2(11)
a = 43 - 22
a =21

==================

Then,

20th term = a + 19d
20th term = 21+ 19(11)
20th term = 21 + 209
20th term = 230

I hope this will help you

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