What is the $n^{th}$ $n^"th"$ term of the geometric sequence $360, 180, 90, 45$ $360,180,90,45$ ?

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Answer 1 · 2017-03-07T20:26:38

$T_{n} = 360 \cdot {(\frac{1}{2})}^{n - 1}$ $T_n = 360*(1/2)^(n-1)$

A GP has the general term $T_{n} = a r^{n - 1}$ $T_n = ar^(n-1)$

In this case we have:

$T_{1} = a = 360$ $T_1 =a = 360$

$r = \frac{T_{n}}{T_{n - 1}} = \frac{45}{90} = \frac{90}{180} = \frac{180}{360} = \frac{1}{2}$ $r = T_n /T_(n-1) = 45/90=90/180 = 180/360 = 1/2$

Substituting these values gives: $T_{n} = 360 \cdot {(\frac{1}{2})}^{n - 1}$ $T_n = 360*(1/2)^(n-1)$

This means that if we want to know the value of a particular term, we just need to plug in the value of $n$ $n$ .

What is the n^"th"nthn^"th" term of the geometric sequence 360,180,90,45360,180,90,45360,180,90,45?