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Question
Choose the correct alternative answer for the following question .
What is the sum of the first 30 natural numbers ?
Options
464
465
462
461
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Solution
The given series is 1 + 2 + 3 + ... + 30
Here,
a = 1
d = 1
n = 30
\[S_n = \frac{n}{2}\left( 2a + \left( n - 1 \right)d \right)\]
\[ S_{30} = \frac{30}{2}\left( 2a + \left( 30 - 1 \right)d \right)\]
\[ = \frac{30}{2}\left( 2\left( 1 \right) + 29\left( 1 \right) \right)\]
\[ = 15\left( 2 + 29 \right)\]
\[ = 15 \times 31\]
\[ = 465\]
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