GP sequence

Find the remaining unknown characteristics in the finite geometric sequence, if given: a1 = 5, an = 320, sn = 635, n =?, q =?

Correct answer:

n =  7
q =  2

Step-by-step explanation:

a1=5 a=320 s=635  a=a1 qn1 s=a1 q1qn1  a q=a1 qn a qa1=a1 (qn1)  s=a1 q1qn1=a1 q1(a qa1)/a1 s=q1a qa1  s (q1)=a qa1 635 (q1)=320 q5  315q=630  q=2  a q=a1 qn a q/a1=qn1 64=2n1 26=2n1 n=6+1=7  n=lnqln(a q/a1)=7
q=2   Verifying Solution:  a2=q a1=2 5=10 a3=q a2=2 10=20 a4=q a3=2 20=40 a5=q a4=2 40=80 a6=q a5=2 80=160 a7=q a6=2 160=320  s7=a1+a2+a3+a4+a5+a6+a7=5+10+20+40+80+160+320=635

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