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bonufazy [111]
3 years ago
11

Which number is rational?

Mathematics
2 answers:
Tatiana [17]3 years ago
6 0

Answer:

The correct option is D.

Step-by-step explanation:

A number is called a rational if it can be written in the form of p/q where p/q are integers and q≠0.

The terminating numbers are always a rational number.

From the given options it is clear that option option D represents a terminating number,

5.33333..=5.\bar{3}

5.33333..=5+\frac{3}{10-1}

5.33333..=5+\frac{3}{9}

5.33333..=5+\frac{1}{3}

5.33333..=\frac{16}{3}

The number 5.3333333... is a rational number.

Therefore the correct option is D.

Vaselesa [24]3 years ago
5 0
Yeah its D i just checked
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Step-by-step explanation:

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Can someone help me and explain step by step
Shkiper50 [21]

Answer:  5) r = 5, 8th term = -78,125

               6) r = 5, 8th term = -312,500

               7) r = 5, {1, 5, 25, 125, 625}

               8) r = 5, {-4, -20, -100, -500, -2500}

<u>Step-by-step explanation:</u>

The explicit formula of a geometric sequence is: a_n=a_1\cdot r^{n-1}, where;

  • n is the number of the term
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  • r is the common ratio

5)\ a_n=-5^{n-1}\\.\qquad =-1\cdot 5^{n-1}\quad \rightarrow \quad a_1=-1\ and\ r=5\\\\a_8=-5^{8-1}\\.\quad =-5^7\\.\quad =-78,125\\\\\\6)\ a_n=-4\cdot 5^{n-1}\quad \rightarrow \quad a_1=-4\ and\ r=5\\\\a_8=-4\cdot 5^{8-1}\\.\quad =-4\cdot 78,125\\.\quad =-312,500

7)\ a_1=1\ and\ r=5\\.\quad a_2=1\cdot 5=\boxed{5}\\.\quad a_3=5\cdot 5=\boxed{25}\\.\quad a_4=25\cdot 5=\boxed{125}\\.\quad a_5=125\cdot 5=\boxed{625}\\\\\\\\8)\ a_1=-4\ and\ r=5\\.\quad a_2=-4\cdot 5=\boxed{-20}\\.\quad a_3=-20\cdot 5=\boxed{-100}\\.\quad a_4=-100\cdot 5=\boxed{-500}\\.\quad a_5=-500\cdot 5=\boxed{-2500}\\\\\\

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