To solve this problem, we need to understand that the sum of an arithmetic series (which the consecutive page numbers form) is given by the formula:

Sum = n/2 * (a + l)

where:
n = number of terms (in this case, the number of pages)
a = first term (the first page number)
l = last term (the last page number)

Given that the sum of the page numbers is 678, we can use this formula to find possible values for n. However, because we don't know the values of a and l, we need to consider possible scenarios.

1. If Ajay started tearing from the first page (a = 1), the last page number (l) would be less than if he started tearing from a later page. In this case, n would be larger.

2. If Ajay started tearing from a later page, a would be larger, l would be larger, and n would be smaller.

So, we need to find values of n that satisfy the equation for some possible values of a and l.

One way to do this is to start with n = 1 and incrementally increase it, each time checking if the sum can be divided evenly by n. If it can, that means there is a possible pair of a and l that would make the sum 678.

Doing this, we find that the possible numbers of pages Ajay could have torn from his book are: 2, 3, 6, 9, 18, 27, 37, 74, 111, 222.

Question

To solve this problem, we need to understand that the sum of an arithmetic series (which the consecutive page numbers form) is given by the formula:

Sum = n/2 * (a + l)

where:
n = number of terms (in this case, the number of pages)
a = first term (the first page number)
l = last term (the last page number)

Given that the sum of the page numbers is 678, we can use this formula to find possible values for n. However, because we don't know the values of a and l, we need to consider possible scenarios.

1. If Ajay started tearing from the first page (a = 1), the last page number (l) would be less than if he started tearing from a later page. In this case, n would be larger.

2. If Ajay started tearing from a later page, a would be larger, l would be larger, and n would be smaller.

So, we need to find values of n that satisfy the equation for some possible values of a and l.

One way to do this is to start with n = 1 and incrementally increase it, each time checking if the sum can be divided evenly by n. If it can, that means there is a possible pair of a and l that would make the sum 678.

Doing this, we find that the possible numbers of pages Ajay could have torn from his book are: 2, 3, 6, 9, 18, 27, 37, 74, 111, 222.

Knowee AI · Accepted Answer

To solve this problem, we need to understand that the sum of an arithmetic series (which the consecutive page numbers form) is given by the formula:

Sum = n/2 * (a + l)

where:
n = number of terms (in this case, the number of pages)
a = first term (the first page number)
l = last term (the last page number)

Given that the sum of the page numbers is 678, we can use this formula to find possible values for n. However, because we don't know the values of a and l, we need to consider possible scenarios.

1. If Ajay started tearing from the first page (a = 1), the last page number (l) would be less than if he started tearing from a later page. In this case, n would be larger.

2. If Ajay started tearing from a later page, a would be larger, l would be larger, and n would be smaller.

So, we need to find values of n that satisfy the equation for some possible values of a and l.

One way to do this is to start with n = 1 and incrementally increase it, each time checking if the sum can be divided evenly by n. If it can, that means there is a possible pair of a and l that would make the sum 678.

Doing this, we find that the possible numbers of pages Ajay could have torn from his book are: 2, 3, 6, 9, 18, 27, 37, 74, 111, 222.

Frustrated with repeated poor scores in English, Ajay tore up some consecutive leaves from his English book. If the sum of the page numbers on the leaves that he tore was 678, the number of pages he tore from the book could be _____. (Assume that each torn leaf is numbered on either side.)

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