Question

the sum of first five terms of an arithmetic sequence is 180 what is the third term of the sequence​

Answer 1

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.

Answer 2

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