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The second term of a convergent series is 5/2 and the sum to infinity is 10. Calculate the constant ratio.

User OneTwo
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1 Answer

3 votes

Answer:

1/2

Explanation:

You want the common ratio of a geometric series whose sum is 10 and whose second term is 5/2.

Second term

For first term a1 and common ratio r, the second term is ...

a2 = a1·r

Sum

The sum to infinity of the series is ...

S = a1/(1 -r)

Solution

Dividing the first equation by the second, we have ...

(5/2)/10 = (a1·r)/(a1/(1-r))

5/20 = r(1 -r)

r² -r +1/4 = 0 . . . . . . put in standard form

(r -1/2)² = 0

The solution is the value of r that makes the factors be zero: r = 1/2.

The constant ratio is 1/2.

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Additional comment

The first term is 5.

User Muthuraj
by
8.2k points

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