Question

If n is odd, then ( 1+3+5+7+.........to n terms) is equal to

Answer 1

Step-by-step explanation:

We have:

1 + 3 + 5 + 7 + ......... + to n terms

where, n is odd number

We have to find, 1 + 3 + 5 + 7 + ......... + to n terms = ?

Solution:

1 + 3 + 5 + 7 + ......... + to n terms

The given series are in AP.

Here, first term (a) = 1, common difference (d) = 3 - 1 = 2

and number of terms (n) = n

We know that,

The sum of up to n terms

⇒

⇒ (2 + (n - 1)2)

⇒ (2 + 2n - 2)

⇒ (2n)

⇒

∴ 1 + 3 + 5 + 7 + ......... + to n terms = n square

Thus, 1 + 3 + 5 + 7 + ......... + to n terms = n square

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Answer 2

Step-by-step explanation:

Sn=(n/2)[(2a)+{(n-1)(d)}]

=(n/2)[(2)+{(n-1)(2)}]

=(n/2)[2-2+2n]

=(n/2)(2n)

=n^2