Find the average of first 30 natural numbers.

Open in App

Solution

Dear Student,

$F i r s t 30 n a t u r a l n u m b e r s a r e - 1, 2, 3, 4, . . . . . . . ., 30 T h i s s e q u e n c e f o r m s a n A . P ., w h e r e, f i r s t t e r m (a) = 1 c o m m o n d i f f e r e n c e (d) = 1 S u m o f n t e r m s o f a n A . P . i s g i v e n b y S_{n} = \frac{n}{2} [2 a + (n - 1) d] S_{30} = \frac{30}{2} [2 (1) + (30 - 1) (1)] S_{30} = 15 [2 + 29] S_{30} = 15 \times 31 S_{30} = 465 A v e r a g e = \frac{S u m o f a l l t h e o b s e r v a t i o n s}{N u m b e r o f o b s e r v a t i o n s} A v e r a g e o f f i r s t 30 n a t u r a l n u m b e r s = \frac{465}{30} = 15.5$

Regards

Suggest Corrections

Similar questions

The average of first $50$ natural numbers is

Join BYJU'S Learning Program