Quantities 60183

Determine the remaining quantities in the finite geometric sequence, given: n = 4, an = 12.5, sn = 187.5, a1 = ?, q =?

Correct answer:

a1 =  100
q =  0.5

Step-by-step explanation:

n=4 a4=12.5 s4=187.5  a4=a1 qn1=a1 q3 s4=a1 q1qn1=a1 q1q41  s4=q3a4 q1q41 s4=q3a4 q1(q21)(q2+1) s4=q3a4 q1(q1)(q+1)(q2+1) s4=q3a4 (q+1)(q2+1)  s4/a4=q3(q+1)(q2+1) s4 q3=a4 (q+1)(q2+1)  q=1 q=1/2=21=0.5  a1=q3a4=213a4=0.5312.5=100
 Verifying Solution:  a2=q a1=21 a1=0.5 100=50 a3=q a2=21 a2=0.5 50=25  s=a1+a2+a3+a4=100+50+25+12.5=2375=18721=187.5  q=21=0.5



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