Question

if sum sigma n= 210,find n

Answer 1

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Answer 2

Answer:  

⇒ n = 20

Step-by-step explanation:

$\sum n = 210\\\\\text{And we know that }\sum n = \frac{n(n+1)}{2}\\\\\implies \frac{n(n+1)}{2}=210\\\\\implies n(n+1)=2\times 210\\\\\implies n^2+n-420=0$

⇒ n² + 21n - 20n - 420 = 0

⇒ n(n + 21) - 20(n + 21) = 0

⇒ (n + 21)(n - 20) = 0

⇒ n = -21 or n = 20

Since, The number of terms cannot be a negative quantity so n = - 21 is rejected.

⇒ n = 20