The sum of first n terms of an A.P. is 50√2. ...

CBSE Class 10 Basic Math 2026 All Sets Solved Paper

Question : 17 of 20

Marks: +1, -0

The sum of first n terms of an A.P. is 50√2. If the first and the last terms are √2 and 19√2 respectively, then the value of n is :

Solution:

Given:

Sum of first n terms

(S_n) = 50\sqrt{2}

First term (a) =

\sqrt{2}

Last term (l) =

19\sqrt{2}

The sum of the first n terms of an A.P. when the first and last terms are known:

S_n = \frac{n}{2} (a + l)

50\sqrt{2} = \frac{n}{2} (\sqrt{2} + 19\sqrt{2})

50\sqrt{2} = \frac{n}{2} (20\sqrt{2})

50\sqrt{2} = 10n \sqrt{2}

10n = 50

n = \frac{50}{10}

n = 5

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