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Salsk061 [2.6K]
4 years ago
11

Mary and her brother John collect foreign coins. Mary has three times the number of coins that John has. Together they have 140

foreign coins.
Mathematics
1 answer:
Crank4 years ago
6 0
Mary has 3x coins, John has x coins,
x+3x=140.
4x=140
x=140/4
x=35

John has 35 coins and Mary has 105 coins.
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If the second term of a geometric sequence of real numbers is -2 and the fifth term is 16 then what is the fourteenth term?
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<h3>Given</h3>

A geometric sequence such that ...

a_2=-2\quad\text{and}\quad a_5=16

<h3>Find</h3>

a_{14}

<h3>Solution</h3>

We can use the ratio of the given terms to find the common ratio of the sequence, then use that to find the desired term from one of the given terms. We don't actually need the common ratio (-2). All we need is its cube (-8).

a_2=a_1r^{(2-1)}=a_1r^1\\a_5=a_1r^{(5-1)}=a_1r^4\\a_{14}=a_1r^{(14-1)}=a_1r^13=a_5r^9\\\\\dfrac{a_5}{a_2}=\dfrac{a_1r^4}{a_1r^1}=r^3=\dfrac{16}{-2}=-8\\\\r^9=\left(r^3\right)^3=(-8)^3=-512\\a_{14}=a_5(-512)\\\\a_{14}=-8192

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