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Question
The sum of all two digit numbers is ______.
Options
9810
9045
4509
4905
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Solution
The sum of all two digit numbers is 4905.
Explanation:
The two digit numbers are 10, 11, 12, 13, ..., 99
Which forms A.P. with first term = a = 10
And d = common difference = 12 – 11 = 1
And l = 99
We know that,
l = Tn
`\implies` 99 = a + (n – 1)d
`\implies` 99 = 10 + (n – 1)
`\implies` 99 = 9 + n
`\implies` n = 90
Since `S_n = n/2[a + l]`
`\implies S_90 = 90/2[10 + 99]`
`\implies` S90 = 45 × 109
`\implies` S90 = 4905
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