Question

45. A pile of logs has 24 logs in the bottom layer, 23 in the second layer, 22 in the third, and so on. The top layer contains 10 logs. Find the total number of logs in the pile.

Answer 1

The total number of logs is 255. You have to add up every number from 10 to 24.

Answer 2

The total number of logs in the pile will be 255.

What is the sum of an arithmetic sequence?

Let a₁ be the first term, L be the last term, n be the number of terms, and d be a common difference.

Then the sum of the arithmetic sequence will be

S = (n / 2)[a₁ + L]

S = (n/2) [2a + (n − 1) d]

A pile of logs has 24 logs in the bottom layer, 23 in the second layer, 22 in the third, and so on. The top layer contains 10 logs.

The common difference is negative 1.

Then the nth term of the arithmetic sequence is given as,

10 = 24 + (n - 1) x (-1)

n - 1 = 14

n = 15

Then the total number of logs in the pile will be

S = (15/2) [24 + 10]

S = 7.5 x 34

S = 255

The total number of logs in the pile will be 255.

More about the sum of arithmetic sequence link is given below.

https://brainly.com/question/25749583

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