the sum of first five terms of an arithmetic sequence is 180 what is the third term of the sequence
Answers
Answer:
36
Step-by-step explanation:
first five term of AP = a, a+d, a+2d, a+3d, a+4d
a+a+da+2d+a+3d+a+4d = 180
5a+10d = 180
5(a+2d) = 180
a+2d = 180÷5
a+2d= 36
a+2d is the third term of AP so the answer is 36.
Step-by-step explanation:
Given :-
The sum of first five terms of an arithmetic sequence is 180.
To find :-
What is the third term of the sequence ?
Solution :-
We know that
The sum of first n terms in an AP is Sn
= (n/2)[2a+(n-1)d]
Now
Sum of the first five terms of the AP
=> S 5 = (5/2)[2a+(5-1)d]
=> S 5 = (5/2)[2a+4d]
=> S 5 = (5/2)×2(a+2d)
=> S 5 = 5(a+2d)
According to the given problem
The sum of first five terms of an arithmetic sequence is 180.
=> 5(a+2d) = 180
=> a+2d = 180/5
=> a +2d = 36
We know that
The nth term of an AP = an = a+(n-1)d
=> a+(3-1)d = 36
=> a3 = 36
Therefore third term = 36
Answer:-
The third term of the given AP is 36
Used formulae:-
→ The nth term of an AP = an = a+(n-1)d
→The sum of first n terms in an AP is Sn
= (n/2)[2a+(n-1)d]
Where,
- a = First term
- d = Common difference
- n = Number of terms