What is the fifth term of the arithmetic sequence whose third term is 29 and whose twenty-ninth term is 289.
The n'th term of an arithmetic progression is given by a + (n-1)d, where a is the first term and d is the common difference. So here we have:
a + (3-1)*d = 29 and
a + (29-1)*d = 289
Subtract the first from the second: 26*d = 260 so d = 10
Put this in the first equation to get a + 2*10 = 29 so a = 9
Hence the fifth term is 9 + (5-1)*10 or 49