Question

How much is the average of all the odd natural Numbers up to 60​

Answer 1

Answer:

Step-by-step explanation:

30 is the answer

Answer 2

Answer:

870

Step-by-step explanation:

To Find:- Average of all odd natural numbers till 60.

Solution:-  

Odd numbers are 1,3,5,7,9,11,.........,59

So, this becomes an AP with first term = 1, common difference = 2, and last term = 59.

As we know, $t_{n}$ = a + (n-1)d , where $t_{n}$ = last term,

                                                          a = first term,

                                                          d = common difference.

∴ 59 = 1 + (n-1) 2

⇒ 59 = 1 + 2n - 2

⇒ 2n = 58

⇒ n = $\frac{58}{2}$

⇒ n = 29

As we know, to find the sum of terms in AP

⇒ $S_{n}$ = $\frac{n}{2}$[2a + (n-1)d], where $S_{n}$ = sum of all terms,

                                             n = total number of terms,

                                             a = first term,

                                             d = common difference,

                                             $t_{n}$ = last term

Also written as, ⇒ $S_{n}$ = $\frac{n}{2}$[a + l]

⇒ $S_{n}$ = $\frac{29}{2}$[1 + 59]

⇒ $S_{n}$ = $\frac{29}{2}$ × 60

⇒ $S_{n}$ = 29 × 30

⇒ $S_{n}$ = 870

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