What is the sum of all odd numbers between 0 and 50?

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625

600

650

700

answer is A.

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Detailed Solution

Given numbers are 0 and 50.
We know that odd numbers between 0 and 50 are

1, 3, 5, 7, … …, 49

. Let the first term be a and the common difference be d, then a = 1.
So, common difference: d = 3 – 1.
i.e., d = 2
Last term is 49.

Take t n = 49 ∴ t n = a + (n − 1) d ⇒ 49 = 1 + (n − 1) 2 ⇒ 49 = 1 + 2 n − 2 ⇒ 49 = 2 n − 1

Therefore,

2 n = 50 ⇒ n = 502 ⇒ n = 25

Formula used for sum of first term of A.P.:

S n = n 2 [a + l]

Applying formula for sum of first n terms of A.P.,

∴ S n = n 2 [a + l] ⇒ S 25 = 252 [1 + 49] = 252 × 50

⇒ S 25 = 25 × 25 = 625

Therefore, the sum of all odd numbers is 625.
Hence, option (1) is correct.

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