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What is the 8th term of the geometric sequence 4, 20, 100,...?

1 Answer

Jun 1, 2018

$a_{8} = 312, 500$ $color(brown)(a_8 = 312,500$

Explanation:

Nth term of geometric sequence $a_{n} = a r^{n - 1}$ $a_n = a r^(n-1)$

$a = 4, a_{2} = 20, a_{3} = 100$ $a = 4, a_2 = 20, a_3 = 100$

$r = \frac{a_{2}}{a} = \frac{a_{3}}{a_{2}} = \frac{20}{4} = \frac{100}{20} = 5$ $r = a_2 / a = a_3 / a_2 = 20 / 4 = 100 / 20 = 5$

$a_{8} = 4 \cdot 5^{8 - 1} = 4 \cdot 5^{7} = 312, 500$ $a_8 = 4 * 5^(8-1) = 4 * 5^7 = 312,500$

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