Observe the following pattern and answer the questions that follow :

1 + 2 + 3 + 4 + 5 = 15

2 + 3 + 4 + 5 + 6 = 20

3 + 4 + 5 + 6 + 7 = 25

(i) By which number should we multiply the middle number to get the sum?

(ii) Write the row of the pattern which gives the sum as 75.

(iii) Can there be any row of the pattern which gives the sum as 92?

(i) Observing the pattern:

1 + 2 + 3 + 4 + 5 = 15. The middle number is 3 and 3 x 5 = 15.

2 + 3 + 4 + 5 + 6 = 20. The middle number is 4 and 4 x 5 = 20.

3 + 4 + 5 + 6 + 7 = 25. The middle number is 5 and 5 x 5 = 25.

The pattern shows that we should multiply the middle number by 5 to get the sum.

(ii) Using the rule from part (i), we can find the middle number for a sum of 75:

Middle number = 75 ÷ 5 = 15.

The row consists of five consecutive numbers with 15 as the middle number.

The two numbers before 15 are 13 and 14.

The two numbers after 15 are 16 and 17.

Hence, the row is 13 + 14 + 15 + 16 + 17 = 75.

(iii) For a sum of 92, the middle number would have to be:

Middle number = 92 ÷ 5 = 18.4

Since the numbers in the pattern are always integers, the middle number must also be an integer. As 92 is not exactly divisible by 5 (it has a remainder of 2), there cannot be a row of this pattern that gives a sum of 92.

Hence, there will not be any row of the above pattern which gives the sum as 92.