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.

Predict the world record for the mile in the year 2010, leaving your answer in seconds.

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.

Predict the world record for the mile in the year 2010, leaving your answer in seconds.

Vocaloid · Answer

Judging by the notation, it wants you to treat the times as an arithmetic sequence

an = a1 + (n-1)d

create two separate equations for n = 1865 and n = 1954
a1865 = a1 + (1865-1)d = 276.5 
a1954 = a1 + (1954-1)d = 239.4

if you subtract the two equations, you can eliminate a1 and solve for d
then you can go back to either equation, plug in d, evaluate a1

finally, from there, you can use the original equation, plug in a1 and n = 2010, d, and solve for an