Question

the 4th term of an ap is 11 and the 11th term is 25 determine the first term and the common difference​

Answer 1

Answer:

a=5, d=2

Step-by-step explanation:

4th term,

a+3d=11

11th term,

a+10d=25

(a+3d=11)-(a+10d=25)

d=2

a+3(2)=11

a+6=11

a=5

Answer 2

Given,

4th term of the AP = 11

11th term of the AP = 25

To Find,

The first term of the AP =?

The common difference of the AP =?

Solution,

From the formula of the nth term in the AP, we have

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

For the 4th term,

$a_4 =a +(4-1)d\\11 =a + 3 d$

a + 3d = 11 ⇒ Equation 1

For the 11th term in the AP, we have

$a_{11} =a +(11-1)d\\25=a + 10d$

a + 10d = 25⇒ Equation 2

Subtracting equation 1 from equation 2

a + 10d - a - 3d = 25 - 11

7d = 14

d = 2

The common difference(d) of the AP is 2

Putting value of d=2 in the equation 2,

a + 10*2 = 25

a + 20 = 25

a = 25 - 20

a = 5

Hence, the first term and the common difference​ of the given AP are 5 and 2 respectively.