Question

In his first trip around a field, a farmer makes 123 bales. In his second trip, he makes 11 fewer bales. Because each trip is shorter than the preceding trip, the farmer estimates that the pattern will continue. Estimate the total number of bales made when there are another five trips around the field.

Answer 1

630

Explanation:

The sum of an arithmetic sequence is given by ...

Sn = n(2a1 +(n-1)d)/2

For the sequence of numbers of bales, we have ...

a1 = 123, d = -11, n = 7

so the total number of bales in 7 trips around the field is ...

S7 = 7(2·123 +6(-11))/2 = 630

The total number of bales made is about 630.

_____

123 + 112 + 101 + 90 + 79 + 68 + 57 = 630