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

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

Answer»

Answer :

COMMON difference , d = -4

★ 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) .

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