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The sum of all the three-digit odd numbers is
1. 1234400
2. 654300
3. 247500
4. None of these

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Correct Answer - Option 3 : 247500

Concept:

Sum of n Terms of AP is given by:

\(\rm s_{n}= \frac{n}{2}[2a + (n - 1)d]\)

Where, a = First term, d = Common difference and n = number of terms

an = nth term = a + (n - 1) d

Calculation:

We can use the concept of arithmetic progression and find the sum of nth term.

Three digit odd numbers are 101, 103, ..., 999

a (first term) = 101, nth term (last term) = 999, d = 2

As we know, an = nth term = a + (n - 1) d

⇒ 999 = 101 + (n - 1) × 2

⇒ 898 =  (n - 1) × 2

∴ n = 450

The formula for finding the sum of nth terms of A.P. is:

\(\rm s_{n}= \frac{n}{2}[2a + (n - 1)d]\)

\(\rm s_{450}= \frac{450}{2}[2 × 101 + (450 - 1)2]\)

\(\rm s_{450}= 225 ×[202 + 449×2]\)

\(\rm s_{450}= 225 ×[202 + 898]\)

\(\rm s_{450}= 225 × 1100\)

\(\rm s_{450}= 247500\)

The list of formulas is given in a tabular form used in AP. These formulas are useful to solve problems based on the series and sequence concept.

General Form of AP a, a + d, a + 2d, a + 3d, . . .
The nth term of AP an = a + (n – 1) × d
Sum of n terms in AP S = n/2[2a + (n − 1) × d]
Sum of all terms in a finite AP with the last term as ‘l’ n/2(a + l)

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