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Delvig [45]
2 years ago
7

Is algebra.

Mathematics
1 answer:
Alja [10]2 years ago
8 0

Answer:

1Q is c

2Q is b

Step-by-step explanation:

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The first, third and thirteenth terms of an arithmetic sequence are the first 3 terms of a geometric sequence. If the first term
Salsk061 [2.6K]

Answer:

The first three terms of the geometry sequence would be 1, 5, and 25.

The sum of the first seven terms of the geometric sequence would be 127.

Step-by-step explanation:

<h3>1.</h3>

Let d denote the common difference of the arithmetic sequence.

Let a_1 denote the first term of the arithmetic sequence. The expression for the nth term of this sequence (where n\! is a positive whole number) would be (a_1 + (n - 1)\, d).

The question states that the first term of this arithmetic sequence is a_1 = 1. Hence:

  • The third term of this arithmetic sequence would be a_1 + (3 - 1)\, d = 1 + 2\, d.
  • The thirteenth term of would be a_1 + (13 - 1)\, d = 1 + 12\, d.

The common ratio of a geometric sequence is ratio between consecutive terms of that sequence. Let r denote the ratio of the geometric sequence in this question.

Ratio between the second term and the first term of the geometric sequence:

\displaystyle r = \frac{1 + 2\, d}{1} = 1 + 2\, d.

Ratio between the third term and the second term of the geometric sequence:

\displaystyle r = \frac{1 + 12\, d}{1 + 2\, d}.

Both (1 + 2\, d) and \left(\displaystyle \frac{1 + 12\, d}{1 + 2\, d}\right) are expressions for r, the common ratio of this geometric sequence. Hence, equate these two expressions and solve for d, the common difference of this arithmetic sequence.

\displaystyle 1 + 2\, d = \frac{1 + 12\, d}{1 + 2\, d}.

(1 + 2\, d)^{2} = 1 + 12\, d.

d = 2.

Hence, the first term, the third term, and the thirteenth term of the arithmetic sequence would be 1, (1 + (3 - 1) \times 2) = 5, and (1 + (13 - 1) \times 2) = 25, respectively.

These three terms (1, 5, and 25, respectively) would correspond to the first three terms of the geometric sequence. Hence, the common ratio of this geometric sequence would be r = 25 /5 = 5.

<h3>2.</h3>

Let a_1 and r denote the first term and the common ratio of a geometric sequence. The sum of the first n terms would be:

\displaystyle \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}.

For the geometric sequence in this question, a_1 = 1 and r = 25 / 5 = 5.

Hence, the sum of the first n = 7 terms of this geometric sequence would be:

\begin{aligned} & \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}\\ &= \frac{1 \times \left(1 - 2^{7}\right)}{1 - 2} \\ &= \frac{(1 - 128)}{(-1)} = 127 \end{aligned}.

7 0
2 years ago
John kept track of how many baskets were made in a basketball game. After 4 minutes, 5 baskets were made.
ivann1987 [24]

1 basket is between 9 and 10 minutes .

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

Here we have , John kept track of how many baskets were made in a basketball game. After 4 minutes, 5 baskets were made.  We need to find How many baskets were made between 9 and 10 minutes . Let's find out:

In order to calculate baskets between 9 min and 10 min we will find baskets at 10 min and at at 9 min , will subtract than !

Baskets at 10 min :

At 4 min we have 5 baskets so , in 10 min

⇒ (10)\frac{5}{4}

⇒ 1.25(10)

⇒ 12.5

Baskets at 9 min :

At 4 min we have 5 baskets so , in 9 min

⇒ (9)\frac{5}{4}

⇒ 1.25(9)

⇒ 11.25

So , Baskets between 10 & 9 min is 12.5-11.25=1.25 , which on rounding off gives 1 . Therefore , 1 basket is between 9 and 10 minutes .

3 0
3 years ago
In one class ,1/6 of the students raked leaves while the rest picked up trash on the playground . what fraction of the students
bixtya [17]
You can do 1-1/6 (1 represents the whole class)

6/6-1/6
=5/6
4 0
3 years ago
Katherine baked a round cake that is 9 inches in diameter. She wants to decorate the cake by putting a piece of ribbon around th
kaheart [24]

Answer:

28.26 inches long of ribbon

5 0
2 years ago
Read 2 more answers
10
shusha [124]

Answer:

B

Step-by-step explanation:

7 0
2 years ago
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