Question

Q.11) If the sum of the A.P. 3, 7, 11,. is 210, the number is terms is

Answer 1

For an A.P,

$S _{n}$ = n/2(2a + (n-1)d)

Here, a = 3, d = 4 

Therefore, 210 = n/2(6 + (n-1)4)
             or, 420 = 6n + $4n^2$ - 4n
             or, $4n^2$ + 2n - 420 = 0
             
Dividing the equation by 2,
  
                  $2n^2$ + n - 210 = 0
              or,(2n + 21)(n-10) = 0 

Therefore, n = -21/2, which is not possible as number of terms cannot be negative.
Therefore, n = 10

Answer 2

Answer:

N=10

Step-by-step explanation:

Number of terms of this A.P are 10