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Step2247 [10]
3 years ago
12

The sum of the digits of a three-digit number is 6. The hundreds digit is twice the units digit, and the tens digit equals to th

e sum of the other two. Find the number.
Mathematics
1 answer:
EleoNora [17]3 years ago
6 0
A+b+c=6, a=2c, b=a+c using a and b in the first equation gives you:

2c+a+c+c=6  now use a=2c again

2c+2c+c+c=6

6c=6

c=1, since a=2c

a=2, since b=a+c

b=3

So the number is 231.
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So your answer is:

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7 0
3 years ago
PLEASE HELP.
OverLord2011 [107]

Answer:

Explicit formula for

1) a_n=17-3(n-1)

2) a_n=(\frac{1}{2} )^{n-1}\cdot 20

Step-by-step explanation:

W have to find the first few terms of the given sequence and then find an explicit equation

Explicit formula = f(n) + d(n-1) , where,

f(n) is first term,

d is common difference,

n-1 is one term less than the term number.

1)

Given : a_1=17\\\\a_{n+1}=a_n-3

\text{We put n =1, we get,}\\\\a_2=a_1-3=17-3=11=17-3(2-1)\\\\\\\text{We put n =2, we get,}\\\\\\a_3=a_2-3=11-3=8=17-3-3=17-3\cdot 2=17-3(3-1)\\\\\text{We put n =3, we get,}\\\\\\a_4=a_3-3=8-3=5=17-3-3-3=17-3\cdot 3=17-3(4-1)\\

Thus, we obtained an explicit formula,

a_n=17-3(n-1)

2)

Given : a_1=20\\\\a_{n+1}=\frac{1}{2} \cdot a_n

\text{We put n =1, we get,}\\\\a_2=a_1-3=17-3=11=17-3(2-1)\\\\\\\text{We put n =2, we get,}\\\\\\a_3=a_2-3=11-3=8=17-3-3=17-3\cdot 2=17-3(3-1)\\\\\text{We put n =3, we get,}\\\\\\a_4=a_3-3=8-3=5=17-3-3-3=17-3\cdot 3=17-3(4-1)\\

Thus, we obtained an explicit formula,

a_n=17-3(n-1)

\text{We put n =1, we get,}\\\\\\a_2=\frac{1}{2} \cdot a_1=\frac{1}{2} \cdot 20=10=(\frac{1}{2} )^{2-1}\cdot 20\\\\\\\text{We put n =3, we get,}\\\\\\a_4=\frac{1}{2} \cdot a_3=\frac{1}{2} \cdot 5=\frac{5}{2}=(\frac{1}{2} )^{4-1}\cdot 20\\\\\\

Thus, we obtained an explicit formula,

a_n=(\frac{1}{2} )^{n-1}\cdot 20

8 0
3 years ago
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