Question

In an AP if the 3rd term is 12 and 50th term is 106 then find its 29th term
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Answer 1

Answer:

a3-12

a50-106

a29-?

a+2d=12

a+49d=106

______–-–--

-47d= -94

d= 2

a+2d=12

a+2(2)=12

a+4=12

a=12-4

a=8

a+29d

8+29(2)

8+56

=62

Answer 2

We know, an= A+(n-1)d

Therefore, a3 = a+(3-1)d =a+2d

Therefore, a50= a+49d

We know that, a+2d=12

Therefore, a=12-2d

2nd eqn

a+49d=106

Putting value of a,

12-2d+49d=106

=12+47d=106

47d=106-12

47d=94

D=94/47=2

D=2

Now, putting value of d in eqn 1

a+2d=12

a+2(2)=12

a+4=12

A=8

Now, we have to find the 29th term, therefore

a29= 8+(28)2

a29= 8+56

A29=64

Therefore, 29th term is 64.

Hope it will help you!

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