This sequence is geometric, what is the next term 500, 250, 125, 62.5,...?

Question

20813 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-11T13:52:07

The next term in the series (5th term) : $=31.25$

$500, 250, 125, 62.5$

When provided with a geometric sequence we must first calculate the common ratio $r:$

$r$ is obtained by dividing a term by its preceding term:

1) $250/500 =1/2$

2) $125/250 = 1/2$
For the sequence the common ratio $r = 1/2$ .

Method 1:
the first term $a = 500$ , and $n = 5$ (We require the 5th term)

The 5th term can be obtained through formula:

$T_n = ar^(n-1) = 500 xx (1/2)^((5-1))$
$= 500 xx (1/2)^4$

$= 500 xx 1/16 = 500/16$

$T_5=31.25$

Method 2
We can find the fifth term by multiplying the 4th term by $r$

$T_5= T_4 xx 1/2$

$= 62.5 xx 1/2$

$= 62.5 /2$

$= 31.25$