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Firdavs [7]
3 years ago
6

given that a1=5 and a2=15 are the first two terms of a geometric sequence, determine the values of a3 and a10. Show the calculat

ions that lead to your answer​
Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
7 0

a_3 is 45 and a_10 is 98415

Step-by-step explanation:

Given

a_1 = 5

a_2 = 15

First of all we have to calculate the common ratio of the sequence. The common ratio is the ratio between two consecutive terms of a geometric sequence.

So,

r=\frac{a_2}{a_1} = \frac{15}{5} = 3

The explicit formula for geometric sequence is:

a_n = a_1.r^{n-1}

Putting the value of r and a_1

a_n = 5.(3)^{n-1}

Putting n=3 in the explicit formula

a_3 =5.3^{3-1}\\= 5 * 3^2\\=5 * 9\\= 45

Putting n=10 for tenth term

a_{10} =5.3^{10-1}\\=5*3^9\\=5 * 19683\\=98415

Hence,

a_3 is 45 and a_10 is 98415

Keywords: Geometric sequence, Explicit formula

Learn more about geometric sequence at:

  • brainly.com/question/10978510
  • brainly.com/question/11007026

#LearnwithBrainly

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Mariabella was 1/4 of the way through her book. Twenty pages later she was 1/3 of the way through her book. When she is 3/4 of t
Alex777 [14]

Answer: 60 pages left.

Step-by-step explanation:

Let the number of pages in the book be x.

As per given, we have

\dfrac14x+20=\dfrac13x\\\\\Rightarrow\ \dfrac{1}{3}x-\dfrac14 x=20\\\\\Rightarrow\ \dfrac{4-3}{12}x=20\\\\\Rightarrow\ \dfrac1{12}x=20\\\\\Rightarrow x=20\times12\\\\\Rightarrow x=240

\dfrac34 of total book = \dfrac34\times 240=180

Pages left = 240-180

= 60

Hence, 60 pages left.

3 0
3 years ago
BRAINLIEST!!
REY [17]

Answer:

Yes, the sum of any two sides is greater than the third.

Step-by-step explanation:

To determine whether the provided sides are the sides of a triangle check if the sum of two sides is more than the third side.

The length provided are: 8.5, 13 and 19.1.

  • Consider the sides 8.5 and 13:

        The sum is:

        8.5+13=21.5

        This sum is greater than the third side 19.1

  • Consider the sides 8.5 and 19.1:

        The sum is:

        8.5+19.1=27.6

        This sum is greater than the third side 13

  • Consider the sides 13 and 19.1:

        The sum is:

         13+19.1=32.1

        This sum is greater than the third side 8.5

Thus, the sides 8.5, 13 and 19.1 are sides of a triangle.

7 0
3 years ago
Read 2 more answers
Mr. Piper is driving Roddy and Scott home from school. They both want to ride in the front seat. How can he make a fair decision
bagirrra123 [75]

Answer:

A.Put each person's name on a separate piece of paper in a bag. Randomly draw the winning name; and D.Roll a number cube. If it lands on an even number, Roddy wins. If it lands on an odd number, Scott wins.

Step-by-step explanation:

In order for it to be a fair decision, both boys have to have an equal chance of being selected.

For choice A, drawing their names from a bag, both names are equally likely to be chosen; that makes this fair.

For choice B, there is 1 way to get both heads when flipping a coin.  There are 2 ways to get heads and tails when flipping a coin.  This gives Scott a greater chance, so this is not fair.

For choice C, there are 2 ways to get a 1 or a 2.  There are 4 ways to get anything else.  This gives Scott a greater chance, so this is not fair.

For choice D, there are 3 even numbers and 3 odd numbers.  Both boys have an equal chance, so this is fair.

5 0
4 years ago
The options are 0.106,0.63,0.51,0.53
Luba_88 [7]
That would be  (20+30+56)/200  =   106/200   = 53/100 Answer
7 0
4 years ago
Read 2 more answers
Which of the following is the number 3.0205 times 10-3 written in standard notation
mr_godi [17]
10^-3 means move decimal place 3 places to left or divide by 1000
move decimal place 3 places left
0.0030205 is normal form
3 0
3 years ago
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