Question

Find the values of s_1 and r for a geometric sequence with s_4= 18 and s_6= 72​

Answer 1

Answer: Choice A

$s_1 = 2.25, \ r = 2$

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Work Shown:

$s_4 = 18\text{ is the fourth term}\\\\s_5 = r*s_4 = 18r\\\\s_6 = r*s_5 = r*(18r) = 18r^2 = 72\\\\\text{So,}\\\\18r^2 = 72\\\\r^2 = \frac{72}{18}\\\\r^2 = 4\\\\r = \sqrt{4}\\\\r = 2$

Use that r value and $s_4 = 18$ to find the first term

$s_n = s_1*(r)^{n-1}\\\\s_4 = s_1*(2)^{4-1}\\\\18 = s_1*8\\\\s_1 = \frac{18}{8}\\\\s_1 = 2.25$

You could use $s_6 = 72$ in place of $s_4 = 18$ (just make sure to use n = 6 instead of n = 4).