Question

answer if you're good in arithmetic progression​

Answer 1

     

What a nice question!!!

The distances between each ball and the bucket are in AP, with first term  a = 5 and the common difference  d = 3.

Which is,

5, 8, 11,......

Because, as the distance between each two adjacent balls is 3 m, the first ball is 5 m away from the bucket, second one is 8 m away from the bucket, third ball is 11m away from the bucket, and so on.

Okay, given that there are 10 balls in total.

The 10th ball is away from the bucket by the distance which is the 10th term of the AP 5, 8, 11,...

So the 10th term = a + 9d = 5 + 9 × 3 = 5 + 27 = 32.

∴ The 10th ball is 32 m away from the bucket.

Now see this carefully.

The competitor has to run 5 m from the bucket to take the first ball.

Then he has to run 5 m again from there to the bucket to drop the ball.

From there he has to run 8 m to the second ball.

Again he has to run 8 m from there to the bucket to drop it.

Then he has to run 11 m to the third one, and then again 11 m to the bucket to drop the third ball.

Here, it seems that, the total distance the competitor has to run, is twice the sum of the distances between each ball and the bucket.

Which is, twice the ''sum of first 10 terms of the AP 5, 8, 11,...''

So the answer is,

$2(5+8+11+...+32) \\ \\ \Rightarrow\ 2(\frac{10}{2}[5+32]) \\ \\ \Rightarrow\ 10 \times 37 \\ \\ \Rightarrow\ \bold{370}$

So the competitor has to run a total of 370 m.

Hope this helps. Plz ask me if you have any doubt on my answer.

Thank you. :-))

#adithyasajeevan