Question

if 3rd term of an ap is 12 and 6th term of An ap is 27 then the common difference is
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Answer 1

Answer:

The answer is that 5

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Answer 2

Answer:

Here, The Common difference of the given A. P. is 5.

Step-by-step explanation:

Here, As per our given question,

3rd term of the A. P. =12=T3

6th term of the A. P.=27=T6

Let the first term of the A. P. be a

Let thecommon difference of the term be d

So, T3=a+(n-1)×d (Where n=3)

=12=a+(3-1)×d

=12=a+2d

=a+2d=12 -(1st)eq.

Now, T6=a+(n-1)×d (Here n=6)

=27=a+(6-1)×d

=27=a+5d

=a+5d=27 -(2nd)eq.

Now on solving both equations by elimination method, we will subtract eq. 2 from 1,

= a+2d= 12

=-a-5d=-27

After solving, we get,

=2d-5d=12-27

=(-3d)=(-15)

=3d=15

=d=15/3

=d=5

By putting the value of in eq. 1,we get,

=a+2×5=12

=a+10=12

=a=12-10

=a=2

Hence, The value of Common difference of the given A. P. =5.

Thank you.