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An infinite geometric series has a common ratio, r. The first term of the series is 10 and the sum to infinity is 50.
(a) Show that the common ratio is 4/5
(b) Find the second term of the series
(c) The first and second terms of the geometric series in part (a) have the same values as the 4th and 8th terms respectively, in an arithmetic series. Find the common difference of the arithmetic series.
An infinite geometric series has a common ratio, r. The first term of the series is 10 and the sum to infinity is 50.
(a) Show that the common ratio is 4/5
(b) Find the second term of the series
(c) The first and second terms of the geometric series in part (a) have the same values as the 4th and 8th terms respectively, in an arithmetic series. Find the common difference of the arithmetic series.
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Verified answer
b₁=10 S=50 q<|1|
a) доказать, что q=4/5.
S=b₁/(1-q)=50
10/(1-q)=50
50*(1-q)=10
50-50q=10
50q=40 |÷50
q=4/5.
b) найти второй член прогрессии:
b₂=b₁*q=10*4/5=8.
b₂=8.
с)
a₄=10 a₁+3d=10
a₈=8 a₁+7d=8
Вычитаем из второго уравнения первое:
4d=-2 |÷4
d=-0,5.
Verified answer
Решение во вложении.