Question

HELP PLS, IM BEGGIN U, I GOT SPESH TEST TOMMOROW :(

Answer 1

• a) x = 8;
• b) The 8th term is 60.75

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We know that the middle term of a GP is the geometric mean of the equidistant terms.

It can be shown as equation:

• (x + 4)² = x(2x + 2)

Solve it for positive value of x:

• x² + 8x + 16 = 2x² + 2x
• x² - 6x - 16 = 0
• x² - 6x + 9 = 25
• (x - 3)² = 25
• x - 3 = 5 and x - 3 = - 5
• x = 8 and x = - 2

The x = - 2 is discarded as negative.

The terms are:

• 8, 12, 18

Find the common ratio:

• r = 12/8 = 3/2

If 8 is the third term then the 8th term is:

• 
  `t_8=t_1*r^7=t_3*r^5=8*(3/2)^5=8*243/32=243/4=60.75`