Question

the 5th term of the ap is 14 and the 12th term of the ap is 35 find the first term and the common difference of AP​

Answer 1

Hi!!

$a5 = 14$

$a12 = 35$

We know the general formula of AP i.e:

$a + (n - 1)d = an$

Now,

$a + (5 - 1)d = 14 \\ a + 4d = 14 - - (1)$

And,

$a + (12 - 1)d = 35 \\ a + 11d = 35 - - (2)$

Solving eq.(1) and (2):

$a + 4d = 14 \\ a + 11d = 35 \\ - - - - - - \\ - 7d = - 21 \\ 7d = 21 \\ d = 3$

Putting the value of 'd' in eq.(1):

$a + 4d = 14 \\ a + 4(3) = 14 \\ a + 12 = 14 \\ a = 14 - 12 \\ a = 2$

So,

The first term is 2 and the common difference is 3.

Thanks a lot!❤

Answer 2

Answer:

First term of AP = a

Common difference = d

5th term of AP = 14

⇒ a + (n-1)d = 14

a + (5-1)d = 14

a + 4d = 14

a = 14 - 4d — (i)

12th term of AP = 35

⇒ a + (n-1)d = 35

a + (12-1)d = 35

a + 11d = 35

a = 35 - 11d — (ii)

Now, we compare equations (i) and (ii):-

Since we know that both the equations stand for the value of ‘a’, we can say that they are equal.

⇒ 14 - 4d = 35 - 11d

-4d + 11d = 35 - 14

7d = 21

d = 3

Now, we find the value of ‘a’ by substituting the value of ‘d’ in equation (i):-

⇒ a = 14 - 4d

a = 14 - 4(3)

a = 14 - 12

a = 2

FIRST TERM OF AP = 2

COMMON DIFFERENCE = 3

Hope it helps

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