Question 1034286
Find x if the sequence 8, x, (5/2)x is geometric. How is this done?
<pre>With this being a GP, we EQUATE terms as follows: {{{matrix(1,2, 2^(nd), term)/matrix(1,2, 1^(st), term)}}}{{{"="}}}{{{matrix(1,2, 3^(rd), term)/matrix(1,2, 2^(nd), term)}}}.
We then get:
{{{x/8 = (5/2)x/x}}}
{{{x/8 = (5x/2)/x}}}
{{{matrix(1,3, x/8 = 5x/2, "÷", x)}}}
{{{matrix(1,3, x/8 = 5x/2, "*", 1/x)}}}
{{{matrix(1,3, x/8 = 5cross(x)/2, "*", 1/cross(x))}}}
{{{x/8 = 5/2}}}
2x = 40 ------- Cross-multiplying
{{{highlight_green(matrix(1,3, x = 40/2, or, x = 20))}}}

Hence, this is a GP, with {{{a[1] = 8}}}, and {{{matrix(1,8, r, or, common, ratio, "=", 20/8, or, 2.5)}}}