Question

The 7th term of an A. P. is 20 and its 13th term is 32 . find an A. P.

Answer 1

Hello !


Here is your answer !


Let a be the first term and d be the common difference

Now

According to the question

a+ 6d = 20..... ( 1 )


a + 12d = 32.... ( 2 )

Now from both the equation

Substract ( 2 ) from ( 1 )

6d = 12
d = 2
Hence the common difference d = 2


Sustitute in ( 1 )

a + 12 = 20

a = 8


Hence The Ap series is 8 , 10 , 12 , 14 , ...



Hope it helps

Answer 2

The required AP. is 8,10,12,14,...

Given;

7th term of an A. P =  20

13th term = 32

To Find;

Ann Arithmetic Progression.

Solution:

The required AP. is 8,10,12,14,...

In AP, we will come across some main terms, which are denoted as:

First term (a)

Common difference (d)

nth Term (an)

Sum of the first n terms (Sn)

As given,

a7 = 20

Then, the formula for nth term of an AP is:

an = a + (n − 1) × d

a7 = a + (7 − 1) x d

a7 = a  +6d =20 ....(1)

and a 13 = a + (13−1) x d

a13 = a +12d = 32 ...(2)

Solving the pair of linear equation (1) and (2), we get:

a + 6d − a − 12d =20−32

⇒−6d = −12

⇒d = 2

Putting the value of d in eq (1), we get

a + 6(2) = 20

⇒a + 12 = 20

⇒a = 8

Therefore, the required AP. is 8,10,12,14,...

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