How do you write the nth term rule for the sequence 1/2,3,11/2,8,21/2,...?

Aug 1, 2016

${T}_{n} = \frac{5 n}{2} - 2$

Explanation:

First decide whether it is an AP or GP.
Subtract consecutive terms.

$\frac{11}{2} - 3 = 5 \frac{1}{2} - 3 = 2 \frac{1}{2}$
$3 - \frac{1}{2} = 2 \frac{1}{2}$

There is the same difference, so it is an AP.

We have the first term, and d.
Sub into the general term.

${T}_{n} = a + \left(n - 1\right) d = \frac{1}{2} + \frac{5}{2} \left(n - 1\right)$

${T}_{n} = \frac{1}{2} + \frac{5 n}{2} - \frac{5}{2}$

${T}_{n} = \frac{5 n}{2} - 2$