According to the 1998 Information Please Almanac, the official speed record for running one mile was held by Richard Webster of England in 1865, with a time of 4 minutes 36.5 seconds.

Roger Bannister, also of England, was the first to run a mile in less than four minutes, clocking a time of 3 minutes 59.4 seconds in 1954.

There are (of course) 60 seconds in each minute. Therefore, we could convert both times into seconds, writing them as follows:

a1865 = 276.5 seconds and a1954 = 239.4 seconds.

Assuming the speeds decrease from year to year in an arithmetic pattern (which they actually have done, more or less), use the information given above to find d.

Question

According to the 1998 Information Please Almanac, the official speed record for running one mile was held by Richard Webster of England in 1865, with a time of 4 minutes 36.5 seconds.

Roger Bannister, also of England, was the first to run a mile in less than four minutes, clocking a time of 3 minutes 59.4 seconds in 1954.

There are (of course) 60 seconds in each minute. Therefore, we could convert both times into seconds, writing them as follows:

a1865 = 276.5 seconds and a1954 = 239.4 seconds.

Assuming the speeds decrease from year to year in an arithmetic pattern (which they actually have done, more or less), use the information given above to find d.

Vocaloid · Answer

consider the two years, 1954 and 1865. if we give each year its own term, there are (1954-1865) + 1 = 90 terms in the sequence

so let's treat a1 as the 1865 time (276.5 seconds) and a90 as the 1954 time (239.4)

plug these into the arithmetic sequence formula an = a1 + (n-1)d. remember, we are treating this as a sequence of 90 so n = 90, an = a90 = 239.4, a1 = 276.5

plug in and solve for d