What is the fifth term of the arithmetic sequence whose third term is 29 and whose twenty-ninth term is 289.

Guest Jun 15, 2017

#1**+1 **

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

.

Alan
Jun 15, 2017