Question

The product of the first three terms of geometric progression is 64.If the first term is a and the common ratio is r;

1. Express r in terms of a
2. Given that the sum of the three terms is 14
   • Find the values of a and r ,hence write down two possible sequences each upto 4th term.
   • Find the sum of the first 5 terms of each sequences.

Answer 1

1. n^th= ar^n-1
   a x ar x ar²=64
   a³r³=64
   r³ =⁶⁴/a³
   r=⁴/a
2.    
   • a + ar + ar2=14
     a+a(4/a) + a(4/a)2=14
     a+ 4+16/a=14
     a2 + 4a + 16 =149 a=2 r=2
     a2-10a + 16 =0 a=8 r=½
     a2 -8a -2a + 16=0
     a(a-8) -2(a-8)=0
     a=2 or 8
     r=4/8 or 4/2 ½or2
     r=½=8,4,2,1,or
     r=2=2,4,8,18
      
   • S50= a(1-rn) r<1
     1-r
     (a(r^n-1) r)/1-r> 1
     (2(s^s-1))/2-1 = 62