Finite geometric sequence

Find the remaining unknown characteristics in the finite geometric sequence, if given: a1 = 18, an = 13122, sn = 19674, n =?, q =?

Correct answer:

n =  7
q =  3

Step-by-step explanation:

a1=18 a=13122 s=19674  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 19674 (q1)=13122 q18  6552q=19656  q=3  a q=a1 qn ln(a q/a1)=n lnq  n=lnqln(a q/a1)=ln3ln(13122 3/18)=7
q=3   Verifying Solution:  a2=q a1=3 18=54 a3=q a2=3 54=162 a4=q a3=3 162=486 a5=q a4=3 486=1458 a6=q a5=3 1458=4374 a7=q a6=3 4374=13122  s7=a1+a2+a3+a4+a5+a6+a7=18+54+162+486+1458+4374+13122=19674

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