Math, asked by shreeyaswaroop8, 4 months ago

The nth term of an AP is 7 – 4n. Find its common difference.

Answers

Answered by AlluringNightingale
6

Answer :

Common difference , d = -4

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) = a + (n - 1)d .

★ If a , b , c are in AP , then 2b = a + c .

★ The sum of nth terms of an AP is given by ; S(n) = (n/2)×[ 2a + (n - 1)d ] .

or S(n) = (n/2)×(a + l) , l is the last term .

★ The nth term of an AP can be also given by ; a(n) = S(n) - S(n-1) .

Solution :

  • Given : nth term , a(n) = 7 - 4n
  • To find : Common difference , d = ?

We know that ,

For an AP , the common difference d is given by d = a(n) - a(n-1) .

Thus ,

→ d = [7 - 4n] - [7 - 4(n - 1)]

→ d = 7 - 4n - 7 + 4(n - 1)

→ d = -4n + 4(n - 1)

→ d = -4n + 4n - 4

→ d = -4

Hence ,

Common difference , d = -4 .

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