Question

Find the first term and the common difference of the A.P. when
its 8th term is 7 and the 11th term is -23​

Answer 1

no idea

Step-by-step explanation:

thanks for free points

Answer 2

Solution

Here in this question , we are given that :-

8th Term of the AP = 7

11th Term of the AP = -23

We know that ,

an = a + (n-1) d

$\implies$ a + 7 d = 7 $\longrightarrow$ (1)

          and

     a + 10 d = -23 $\longrightarrow$ (2)

Here the Equations are Linear Equations in one variable , so we can solve it by elimination method .

a + 7 d = 7

a + 10 d = - 23

On Multiplying (2) by -1 ,

a + 7 d = 7

-a - 10d = 23    

   - 3 d = 30

$\red\bigstar\sf Therefore , Common\; Difference (d) = \dfrac{30}{-3} = -10$

To Obtain The value of The First Term (a) , we can simply substitute the value of d in any of the two equations .

Here let's substitute in (1) , then

a + 7 × -10 = 7

a - 70 = 7

a = -63

$\sf \red \bigstar First Term (a) = - 63$