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

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Answer 1 · 2016-08-01T23:34:56

$T_n = (5n)/2 -2$

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

$11/2-3 =5 1/2-3 = 2 1/2$
$3-1/2 = 2 1/2$

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

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

$T_n = a+ (n-1)d = 1/2 + 5/2(n-1)$

$T_n = 1/2 + (5n)/2 - 5/2$

$T_n = (5n)/2 -2$

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