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 q  a1 = a1  (qn 1)  s = a1 q1qn1 =  a1 q1(a q  a1) / a1 s = q1a qa1  s (q1)=a qa1 635 (q1)=320 q5  315q=630  q=315630=2  q=2  a q = a1  qn a q/a1= qn1 64 = 2n1 26 =2n1 n=6+1=7  n =  lnqln (a q/a1)
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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