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Question
What is the sum of an odd numbers between 1 to 50?
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Solution
The odd numbers between 1 to 50 are
1, 3, 5, ......, 49
The above sequence is an A.P.
∴ a = 1
∴ d = 5 – 3 = 2
Let the number of terms in the A.P. be n.
Then, tn = 49
Since tn = a + (n – 1)d,
49 = 1 + (n – 1)(2)
∴ 49 = 1 + 2n – 2
∴ 49 = 2n – 1
∴ 49 + 1 = 2n
∴ n =`50/2`
∴ n = 25
Now, `S_n = n/2 (t_1 + t_n)`
∴ `S_25 = 25/2 (1 + 49)`
= 12.5 × 50
= 625
∴ The sum of odd numbers between 1 to 50 is 625.
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