Question 85

Sita starts to calculate sum of all odd natural numbersi less than 72. What result does she get'?

Solution

Odd natural numbers less than 72 = 1, 3, 5, 7, 9.......71

Here, a = 1 and common difference = 2

Number of terms = n

And nth term is 71.

So,

71= a + (n - 1)d

⇒ 71 = 1 + (n - 1)2

⇒ 71 - 1 = 2n - 2

⇒ 70 + 2 = 2n

⇒ n = 72/2

⇒ n = 36

Now, sum of n number of terms = Sn = n/2{2a +(n - 1)d}

$$S_{36} = 36/2 \times ({{2 \times1 + (36 -1)2}})$$

$$= 18 \times ({2 + (35\times2)})$$

$$= 18\times72$$

1296

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