Question

the first three terms of a sequence are given. write your answer as a decimal or whole number. round to the nearest thousandth (if necessary). 32,16,8,... find the 9th term.

Explanation:

Step1: Identify sequence type

This is a geometric sequence where each term is half the previous one. The first term $a_1 = 32$, common ratio $r = \frac{16}{32} = \frac{1}{2} = 0.5$.

Step2: Use geometric sequence formula

The formula for the $n$-th term of a geometric sequence is $a_n = a_1 \times r^{n-1}$.

Step3: Substitute n=9 into formula

$a_9 = 32 \times (0.5)^{9-1}$

Step4: Simplify the exponent

$(0.5)^8 = 0.00390625$

Step5: Calculate the final value

$a_9 = 32 \times 0.00390625$

Answer:

0.125