Find the 8th term of the geometric sequence 5,20,80,...​

SOLUTION:Step 1: List the given values.[tex]\begin{aligned} & n = 8 \\ & a_1 = 5 \\ & a_2 = 20 \\ & a_3 = 80 \end{aligned}[/tex]Step 2: Find the common ratio.[tex]\begin{aligned} r & = \frac{a_2}{a_1} = \frac{a_3}{a_2} \\ r & = \frac{20}{5} = \frac{80}{20} \\ r & = 4 = 4 \end{aligned}[/tex]Step 3: Solve for the 8th term of a geometric sequence.[tex]\begin{aligned} a_n & = a_1r^{n - 1} \\ a_8 & = (5)(4)^{8 - 1} \\ & = 5(4)^7 \\ & = 5(16,384) \\ & = \boxed{81,920} \end{aligned}[/tex]Hence, the 8th term of a geometric sequence is 81,920.

Answered by GreatRedSpot | 2024-09-02