Cari Bean was on her way to the islands in her yachet. Because of the waves and the currents, she was making irregular progess. The first day she traveled 100 miles. The second day she traversed 120 miles, and the third day only 90 miles. On the fourth day she made 110 miles, and on the fifth day, 80 miles. If this trend continues, how many miles will she have traveled in ten days?

Question

Cari Bean was on her way to the islands in her yachet.  Because of the waves and the currents, she was making irregular progess.  The first day she traveled 100 miles.  The second day she traversed 120 miles, and the third day only 90 miles.  On the fourth day she made 110 miles, and on the fifth day, 80 miles.  If this trend continues, how many miles will she have traveled in ten days?

Steve · Answer

I don't see much of a trend. In five days, she has gone 500 miles.

At that overall rate, she will have gone 1000 miles in 10 days.

On the other hand, her differences from day to day have been +20 -30 +20 -30. If that pattern continues, she'll have gone 100+ [800+4(-10)] + [100+20] = 980 miles.