Question

If first 15 terms of an AP is 180 then 5th term of that AP is:​

Answer 1

Answer:

12

Step-by-step explanation:

Correct Question :-

If the sum of the arithmetic series of 15 terms is 180, then what is the 8th term?

Given,

Sum of first 15 terms of an A.P(S_15) = 180

To Find :-

8th term of an A.P

How To Do :-

As they given the value of the sum of first 15 terms of an A.P , we need to substitute the formula in that equation and we need to equate it to '180'.We need to simplify that and we need to consider it as equation. Then we need to find the equation of 8th term and we need to substitute the value of that considered equation here and we need to find the value of '8'th term.

Formula Required :-

Sum of 'n' terms of an A.P :-

$S_n=\dfrac{n}{2}[2a+(n-1)d]$

nth term of an A.P :-

$a_n=a+(n-1)d$

Solution :-

S_15 = 180

$\dfrac{15}{2}[2a+(15-1)d]=180$

$\dfrac{15}{2}[2a+(14)d]=180$

$\dfrac{15}{2}[2a+14d]=180$

$\dfrac{15}{2}\times 2[a+7d]=180$

15[a + 7d] = 180

a + 7d = 180/15

a + 7d = 36/3

a + 7d = 12

[ Let it be equation - 1]

7th term of an A.P :-

a_8 = a + (8- 1)d

a_7 = a + 7d

Substituting the value of equation - 1 in the above equation :-

a_7 = 12.

∴ Seventh term of an A.P = a₇ = 12.