Question

If sigma n=45, then n=
(3) 11 (4) 12 (2) 10 (1) 9​

Answer 1

Option (1) 9 is the correct answer.

Given:

∑n = 45

To Find:

The value of n

Solution:

Sigma is used to denote the sum of similar terms. Sigma is generally used in the summation notation. Instead of writing long sums, Sigma ∑ is represented.

∑n = n(n+1) / 2

45 = n(n+1) /2

⇒ n²+ n =90

⇒n²+ n -90=0

⇒ n² + 10n -9n -90 =0

⇒ n(n+10) -9(n+10) =0

⇒(n+10)(n-9)=0

n+10 = 0 ⇒ n=-10

n-9 =0 ⇒n=9

∴ Option (1) 9 is the correct answer.

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Answer 2

Answer:

Option (1) is correct.

Step-by-step explanation:

Consider the summation as follows:

$\sum n=45$ ...... (1)

We know that the value of $\sum n$ is $\frac{n(n+1)}{2}$.

From (1),

⇒ $\frac{n(n+1)}{2}=45$

Solve the equation as follows:

$n(n+1)=90$

⇒ $n^2+n=90$

⇒ $n^2+n-90=0$ ...... (1)

Using middle term splitting, solve the quadratic equation as follows:

⇒ $n^2+10n-9n-90=0$

⇒ $n(n+10)-9(n+10)=0$

⇒ $(n-9)(n+10)=0$

⇒ $n=9$ and $n=-10$

Therefore, the value of $n$ is $9$ and $-10$.

Option (1) is correct.

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