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