Question

the 7 term of an Ap is -4 and it's 13 term is -16 find the ap​

Answer 1

Step-by-step explanation:

this may be the right answer

Answer 2

Given :

The 7th term of an AP is -4 and the 13th term is -16.

To Find :

The AP.

As it is given that the 7th term is -4, it can also be written as :

⟹ a + 6d = -4... (1)

And it is also given that the 13th term is -16, which can be written as :

⟹ a + 12d = -16... (2)

Now, using elimination method, lets find the values of a & d.

Have a look at the attachment!

$\sf{ - 6d = 12}$

$\sf{d = \frac{12}{ - 6}}$

$\boxed{\sf{\blue{d = - 2}}}$

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Let us now substitute the value of d in (1),

$\sf{a + 6d = - 4}$

$\sf{ a + 6( - 2) = - 4 }$

$\sf{ a - 12 = - 4 }$

$\sf{ a = - 4 + 12}$

$\boxed{ \sf{ \red{a = 8}}}$

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We found the values of a and d, let us now find the AP.

First term of AP = a

⟹ a = 8.

Second term of AP = a + d

⟹ 8 + ( -2 ) = 6

Third term of AP = a + 2d

⟹ 8 + 2 ( -2 ) = 4

Fourth term of AP = a + 3d

⟹ 8 + 3 ( -2 ) = 2

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