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