The nth term of an A.P. -3,-7,-11,-15,.............. is *
Answers
Answer:
Step-by-step explanation:
Nth term of an AP is a+(n-1)d,
Where a=first number and d=common difference
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Answér :
a(n) = 1 - 4n
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 .
★ 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 ] .
★ The nth term of an AP can be also given by ; a(n) = S(n) - S(n-1) .
★ A linear polynomial in variable n always represents the nth term of an AP .
★ A quadratic polynomial in variable n always represents the sum of n terms of an AP .
★ If each terms of an AP is multiplied or divided by same quantity , then the resulting sequence is an AP .
★ If same quantity is added or subtracted in each term of an AP then the resulting sequence is an AP .
Solution :
- Given :– AP = -3 , -7 , -11 , -15 , . . .
- To find :– nth term , a(n) = ?
Here ,
The given AP is -3 , -7 , -11 , -15 , . . .
Now ,
Common difference will be ;
=> d = a2 - a1
=> d = -7 - (-3)
=> d = -7 + 3
=> d = -4
Now ,
The nth term of the given AP will be ;
=> a(n) = a1 + (n - 1)d
=> a(n) = -3 + (n - 1)(-4)
=> a(n) = -3 - 4n + 4
=> a(n) = 1 - 4n