Question

Plz solve this with great Explanation.
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Answer 1

Question:

If a(n) = 5 - 11n , then find the common difference .

Answer:

d = -11

Note:

• An AP is a type of sequence in which the difference between its consecutive terms are same.

• The common difference for an AP is given as;

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

In general,

d = a(n) - a(n-1) ,

where a(n) is the nth term of the AP.

Solution:

It is given that,

The nth term of the AP is;

a(n) = 5 - 11n

We know that,

The common difference for an AP is given as;

=> d = a(n) - a(n-1)

=> d = {5 - 11n} - {5 - 11(n-1)}

=> d = 5 - 11n - 5 + 11(n-1)

=> d = 11(n-1) - 11n

=> d = 11(n-1-n)

=> d = 11•(-1)

=> d = -11

Hence,

The common difference of the AP is (-11).

Answer 2

Answer:

d = - 11

Explanation:

→ nth term [ a( n ) = 5 - 11n ]

So

→ D = a ( n ) - a ( n - 1 )

→ D = ( 5 - 11n ) - ( 5 - 11 ) ( n - 1 )

→ D = 5 - 11n - 5 + 11 ( n - 1 )

→ D = 11 ( n - 1 ) - 11n

→ D = 11 ( n - 1 - n )

→ D = 11 * ( - 1 )

→ D = - 11

Therefore , - 11 is the answer.