A geometric sequence with six members has the sum of all six members equal to 63; the sum of the even members (that has an even index) has a value of 42. Find these members.

Correct answer:

a1 =  1
a2 =  2
a3 =  4
a4 =  8
a5 =  16
a6 =  32

Step-by-step explanation:

a1+qa1+q2 a1+q3 a1+q4 a1+q5 a1=63 qa1+q3 a1+q5 a1=42  a1+q2 a1+q4 a1=6342=21  qa1+q3 a1+q5 a1a1+qa1+q2 a1+q3 a1+q4 a1+q5 a1=4263  q+q3+q51+q+q2+q3+q4+q5=4263 2(1+q+q2+q3+q4+q5)=3(q+q3+q5) 2+2q2+2q4=q+q3+q5  q=2  a1=21/(1+q2+q4)=21/(1+22+24)=1
a2=q a1=2 1=2
a3=q a2=2 2=4
a4=q a3=2 4=8
a5=q a4=2 8=16
a6=q a5=2 16=32   Verifying Solution:  s1=a1+a2+a3+a4+a5+a6=1+42+4+8+16+32=63 a2=a2+a4+a6=42+8+32=42

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