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goodula
@goodula
July 2022
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Найти q и n геометрической прогрессии, если:
Sn=165; X1=11; Xn=88
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barracuda1313
Verified answer
Xn=X1*q^(n-1)
88=11*q^(n-1)
q^(n-1)=8
Sn=b1*(q^n - 1)/(q-1)
Sn=b1*(q^(n-1)*q-1/(q-1)
165=11*(8*q-1)/(q-1)
15=(8q-1)/(q-1)
15(q-1)=8q-1
15q-15=8q-1
15q-8q=15-1
7q=14
q=2
q^(n-1)=8
2^(n-1)=2^3
n-1=3
n=4
4 votes
Thanks 8
barracuda1313
b1 это Х1
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Answers & Comments
Verified answer
Xn=X1*q^(n-1)88=11*q^(n-1)
q^(n-1)=8
Sn=b1*(q^n - 1)/(q-1)
Sn=b1*(q^(n-1)*q-1/(q-1)
165=11*(8*q-1)/(q-1)
15=(8q-1)/(q-1)
15(q-1)=8q-1
15q-15=8q-1
15q-8q=15-1
7q=14
q=2
q^(n-1)=8
2^(n-1)=2^3
n-1=3
n=4