Question

the common difference of an ap is 5 then find the difference between the 15th term and the 11th term​

Answer 1

Answer :

a(15) - a(11) = 20

Note :

★ A.P. (Arithmetic Progression) : A sequence in which the difference between the consecutive terms are equal is said to be in A.P.

★ If a1 , a2 , a3 , . . . , an are in AP , then

a2 - a1 = a3 - a2 = a4 - a3 = . . .

★ The common difference of an AP is given by ; d = a(n) - a(n-1) .

★ The nth term of an AP is given by ;

a(n) = a1 + (n - 1)d .

Solution :

• Given : Common difference , d = 5
• To find : a(15) - a(11) = ?

We know that ,

The nth term of an AP is given by ;

a(n) = a + (n - 1)d , where a is the first term and d is the common difference of the AP .

Thus ,

=> a(15) = a + (15 - 1)d

=> a(15) = a + 14d

Also ,

=> a(11) = a + (11 - 1)d

=> a(11) = a + 10d

Clearly ,

We have d = 5 . Since the common difference d = 5 is positive , hence the AP is increasing .

Thus , a(15) > a(11)

Thus ,

The difference between the 15th term and 11th term will be given as ;

=> a(15) - a(11) = (a + 14d) - (a + 10d)

=> a(15) - a(11) = a + 14d - a - 10d

=> a(15) - a(11) = 4d

=> a(15) - a(11) = 4×5 { °•° d = 5 }

=> a(15) - a(11) = 20

Hence ,

a(15) - a(11) = 20

Answer 2

Answer:

20

Step-by-step explanation:

The common difference of an ap is 5 (d = 5).

an = a + (n - 1)d

→ a15 = a + (15 - 1)d

→ a15 = a + 14d ...............(1)

Also,

→ a11 = a + (11 - 1)d

→ a11 = a + 10d ................(2)

We have to find the difference between the 15th term and the 11th term.

→ a15 - a11 = (1) - (1)

→ a15 - a11 = (a + 14d) - (a + 10d)

→ a15 - a11 = a + 14d - a - 10d

→ a15 - a11 = 4d

→ a15 - a11 = 4(5)

→ a15 - a11 = 20

Hence, the difference between the 15th term and the 11th term is 20.