Another way to look at this sequence is to try to relate the value of any term Tn to its place number n in the list. In a table, the sequence is as follows:
∴ Tn = 5 × n − 2 = 5n − 2 Tn = 5n − 2 is the value of the nth term of the sequence and is known as the general term. This is a very powerful formula for a sequence as it enables you to: 1. Find the value of any term in the list To fi nd the value of a term, simply replace n by the number of the term. To fi nd the value of the 37th term in the sequence Tn = 5n − 2, replace n with 37.
T37 = 5 × 37 − 2 = 183 The 37th term is 183.
2. Find the position of a term in the list, given its value
Using the sequence above, fi nd which term has a value of 158. Since 158 is some term in the list it must have a name (label). Call this Tn . Tn = 158 = 5n − 2 5n = 160 n = 32
The 32nd term in the list has a value of 158. In general, it is very diffi cult to fi nd a general term Tn for a sequence, given its fi rst few terms.
